15 Mind Blowing Math Facts Insane but True

I'm going to do something that's never been done before, ever in history, and you are going to witness it already there. This is probably the first time that deck of cards has ever been arranged in this specific order in history. First time, think, of all the decks of cards being shuffled around the world right now. Think of all the decks of cards shuffled around the world throughout history, every gunslinger saloon, every poker night, every game of go fish, even taking into account every casino game ever played, every cheesy magic trick you've ever seen every time you played solitaire on your computer. Even considering all of that, given the law of probability, the order of the cards in this deck has probably never occurred before in the history of the universe and probably never will again. Sounds crazy, right? Let's find out why. Welcome to the white files, where smart folks like us get together to talk dirty, and today we're talking about math facts that seem to defy logic. Your hair defies logic. What is what is what? You look like one man boy band who got old. What's on your head? Hair product. Hair product of. Glad got scales. Can just get through this intro please. Go ahead. Grandpa Timberlake, do you think math is everywhere. It's the source code of the universe. It's the blueprint for everything. And most of the time math makes perfect sense. Right? Two plus two is four. Five times five is twenty five five. But sometimes math just gets weird, like the deck of cards, which is bananas by the way. And we'll get to that later in the video. First, we need to ease into it with couple of crazy math facts. Ok, here's one. How many people do you need to get together if you find two that have the same birthday? Here's hint. Not that many in random group of only twenty three people, the chances of two of them sharing the same birthday is fifty percent. This is called the birthday paradox or the birthday problem, because it's not literally paradox, but it's definitely unintuitive when you first hear it at least was for me. So why does it seem so weird? Well, it turns out we're all little self-centered, aren't we? Much little snowflakes. So the first thing we want to do is compare our own birthday against the other twenty two people in the room. That's not how you do it. It's only twenty two chances to find match. The chances are not that high. Instead, what we do is compare all twenty three birthdays against each other. That gives us one, two plus twenty one plus twenty and so on and so on. Ultimately two hundred and fifty three comparisons given that there are usually three hundred and sixty five days in year, two hundred and fifty three chances to find birthday match. It's 50 percent now. Just throw sixty people in row. Chances of finding birthday buddy's ninety nine percent. Now there's an actual formula for this which cannot explain, but can link it in the description below. Here's another one that broke my brain at first. Let's say you have rope wrapped around the earth at the equator. The length of the rope is going to be about twenty five thousand miles long, right? Forty five thousand kilometers. Let's say you want that rope to hover one foot off the ground. Thirty centimeters. How much more rope do you need to add that whole thing to make that happen? The answer, six point to eight feet. One point nine one meters. That's it. That's it. OK, OK, that's weird enough. Right? But here's where the puzzle takes the express train to crazy town. OK, the earth is really big. So let's try the puzzle with something really small, like tennis ball. How long rope to get around the tennis ball? Eight inches. Twenty centimeters to now do the same thing. We want that rope to hover one foot above the tennis ball. How much more rope do we need to add? Same answer. Six point to eight feet. You're sure? I'm sure. So what's going on here? Why does this seem so wrong? Well, it's just the way we picture things in our minds when we talk about huge objects like the planet, our minds shift into kind of large number mode. We expect the answer to the puzzle to be large. Then when we take the same puzzle, apply it to small object. Our brains shift into small number mode and we want the answer to the puzzle to be small. But the catch to this math weirdness is actually kind of obvious. It doesn't matter what size circle we start with, the formula for circumference is two times pi times the radius, whether our circle of ropers around an atom or the earth or the entire universe itself, it doesn't matter when you increase the radius by one foot. The answer is always going to be the same. It's one foot times two. It's two three times pi, three point one four. So we've got two feet times three point one four is six point to eight feet. Every time when first saw this blew my mind OK, OK, let's take break from calculations. want to show you some really cool math patterns. When was seven or eight years old, my grandma told me to write down the sentence. Now don't know why I'm writing, but she was batty lady. And when she said do something, you did it because something cool was about to happen and it totally did. write down the phrase and she says it's spelled the same way backwards. This was the phrase man, plan, canal, Panama. It's palindrome. Palindrome is word or phrase and spelled the same way backwards and forwards. And this is famous one. And there are all kinds of other famous palindromes like Madame in Eden. I'm Adam or Bob is palindrome, but we're going for something little more impressive. But please don't know. couldn't get myself out. go on with the thing, the palindrome, whatever numbers can be palindromes to the numbers. Forty four, five, twenty five, 1001, same backwards and forwards. You get the idea. Here is cool trick. Take the number one square it. The answer is palindrome. It's single digit so it's not an impressive. But I'm going to impress you but promise I'll take two. No one's eleven to the comic book. One one times one one equals one hundred and twenty one one two one palindrome. But it gets crazier. Take three. No one's one hundred and eleven one one one times one one one equals twelve thousand three hundred twenty one which is one two three two one which is palindrome. But here is how to blow your friend's minds. Check it out, pick any number from one tonight. Write down that many ones. So in our case, let's say seven one million one hundred eleven thousand one hundred eleven square that. Watch how fast get this answer. One trillion. Two hundred and thirty four billion. Five hundred and sixty seven million. Six hundred and fifty four thousand three hundred and twenty one. That's palindrome. The front half of our answer will start at one and count up to the number of digits we started with in our case seven. And then the back half of the answer will count down from seven, ending at one side note, if you try this with more than nine digits, the palindrome breaks. The magic only happens with the numbers one through nine. But there's all kinds of other palindromes in math phrases, equations, formulas, all kinds of cool stuff. We're not talking about those here, but the links are Downbelow. Look at that. We made history again. Here's hint. It has to do with factorial. It's coming up nice or mysterious. They got the whole thing going on. Here's what want you to take nine, multiply it by number, any number you want, reduce that answer down to single digit. That digit will always be nine every time. No matter what happens, it is always nine. Let me show you how this works. Nine times five is forty five. Four plus five equals nine. Easy right now. Nine times one hundred and one. That's nine hundred and nine nine zero plus nine equals eighteen. Remember we need single digit so we keep going. One plus eight equals getting the hang of it. All right, let's go bonkers now. Let's go crazy. Nine times the number of days in the year three. Sixty five times the number of bones in the human body. Two hundred, six times the number of Marvel MCU movies. Twenty three. didn't say good ones. just total. The answer is fifteen million five hundred sixty four thousand three hundred thirty one plus five is six plus that next five brings you to eleven plus your next six gives you seventeen at four, twenty one at three or twenty four. The next three brings to twenty seven at zero zero gives you twenty seven single digit, two plus seven equals nine. Now if you want to challenge me on how many days there are in year or bones in the body or number of MCU movies, that's cool. You do you. But whatever numbers you plug in and multiply by nine, your single digit is going to be nine every time. Go ahead and try. Nines get crazier. Now, the trick I'm about to show you, when first saw it, went blind for three hours and everything smelled like peanuts. I'm just joking. You're going to be fine, but it's whole rabbit hole. So just hang in there. Take our magical nine square it nine times nine is 81. Now, divide that into one. The answer is zero point. And then all the single digits from zero to nine in order repeating forever. But we always skip your starting number minus one in this case, eight eight never happens in the sequence, but all the other digits are there in order. Zero point zero one two three four five six seven skip eight nine. And then it repeats again and again on and on forever. And it gets crazier. Let's keep going. Let's take two nines. Ninety nine squared. The answer is nine thousand eight hundred and one. Divide that into one. The answer is zero point and then every two digit number in order from zero zero zero one zero two all the way up to ninety nine and then repeats forever again. But again we skip the starting number minus one. So in this case ninety nine minus one is ninety eight. That never shows up in the sequence, but all the other numbers do in order always and forever. So does it work if we keep going. Yup. Let's do nine nine nine squared. That's nine hundred ninety eight thousand and one divide into one. The answer is zero point and now every three digit number in order from zero zero zero through nine nine nine repeating forever. And just like before we skip your starting number minus one nine nine nine minus one is nine nine eight. That never shows up in the sequence. This will work with four nines, five nine just on and on. And was so amazed by this that wanted to look up like how it works. OK, so here we go. There is. All right, cool. there's actually straightforward reason. Right? OK, let's see. OK, that's not straightforward to me. But if any of that makes sense to you, let me know in the comments below because I'm taking you to Vegas or I'm selling you to the circus. Either way, great channel called No File did video on how this works and there's whole formula behind it. So the link is, well, where it always is. And when you try this yourself, most calculators or even Google won't give you enough digits to see the pattern. Instead, they may give you what's called notation, which is type of scientific notation, which is form of shorthand. But there are some online calculators that will give you big, big numbers. And will link to my favorite in the description. Exponential progression or exponential growth is defined as way that quantity, given common rate of change, increases or decreases over time. Let's warm up with quick puzzle. We'll see how it works. Now, want you to give me your answer as quickly as you can. No pausing just far away here goes in lake. There's patch of blue kneepads. Now, every day the patch doubles in size if it takes forty eight days for the patch to cover the entire lake. How many days before half the lake is covered? Hellfish, what do you got. Twenty four. What do did wrong. The answer is forty seven. I'll think about it. If the size of the patch doubles every day and fills the lake on day forty eight, that must mean that half the lake was covered just the day before day forty seven. That just blew my tidy soulsby mind. When our brains are solving problems like this, we have two modes intuitive and deliberative, fast and slow. At first glance, twenty four makes sense because twenty four is half of forty eight. It's really easy math problem to solve and our brains love solving problems quickly. We're dopamine junkies and the faster we get that dopamine the better. But when we slow down and focus on the premise, the answer is obviously forty seven. And when we realized we didn't earn that dopamine, our brains punish us with frustration. Now, why this happens isn't fully understood, but some experts believe that our brains are punishing us in order to condition us to think more slowly and more logically. Now we've got video coming up on dopamine and other neurotransmitters. Fascinating. So please make sure you like subscribe. Hit the bell, all the business side as you do. Twenty four or forty seven. Be honest. If you said forty seven right off the bat, that means your deliberate reasoning is far above average, far above mine. Let me know in the comments below. did OK, exponential growth. What is that. Well, it's defined as how quantity increases over time when the rate of change is proportional to the quantity itself. In the case of the lilypad, we express that by starting with the number one and just doubling it one, two, four, eight, 16 and so on. This type of growth can also be described as geometric progression with common ratio of two, meaning you take the last number in your series multiplied by two, get your next number and keep on trucking. These numbers can get really big really quickly. And there's lot of well-known examples and parables and histories and stories, all kinds of stuff that talks about this, the chest in the rice like we do. But want to illustrate exponential growth with something that made my brain tissue itchy and it smelled like cheese little bit. don't know why was using, but that's that's typical. It's happening now. All right. This is normal piece of paper. It's about ten millimeters thick now. You fold this in half. The thickness is now twenty millimeters. It's full in half again. Forty millimeters and so on and so forth. Because of the size of the paper, the most number of folds you can get by hand is like six or seven unless you're Thore and maybe you can get few more, but sooner or later you're going to run out of strength or you run out of paper. But what if we had theoretical piece of paper that was infinitely long and infinitely wide, but still only ten millimeters thick? How many times would you have to fold it? Before it was one kilometer high. Just twenty three folds at 30 folds, that stack of paper will be one hundred kilometers high. That means we're in space people. Let's keep folding at 40 to fold. You reach the moon. Fifty one folds, get you all the way to the sun. How many times would you have to fold single sheet of paper that would create stack so high that you could reach the end of the observable universe, which is ninety three billion light years away? How many folds? You'd only have to fold the paper? One hundred and three times. Exponential growth can create some really big numbers. But you know what? Those numbers are nothing compared to what we're going to talk about next factorial. And that's where our deck of cards comes into play. Get my agent on the phone. This is Bush league bullshit. There are bunch of different formulas and explanations describing all of these concepts. will link them below, but in the paper folding example, we were doubling. Our numbers are multiplying by common ratio of two. Multiplying by two is doubling. Right, right. But what happens to the numbers in sequence when instead of multiplying by two, we multiply by the next number in the sequence? That's factorial in written math. factorial is represented as the number, followed by an exclamation point. And that's for good reason. Factorial are crazy. Here's how they work. Let's say you want factorial of five. You take five, multiply by four, multiply by three by two by one. Hellfish would you get headache? The answer is one hundred and twenty. Check it out five times. Four times. Three times two times one one twenty two factorial of six is going to be one twenty times six or in other words six times. Five times. Four times. Three times two times one. You see where we're going with us. The numbers scale really fast. small number factorial can be huge answer. For example, ten factorial seconds is six weeks. That's three million six hundred twenty eight thousand eight hundred seconds. And what's even weirder is it's not five weeks and change or six weeks in bit. Ten factorial seconds is six weeks on the nose. How did they do that? So what effect tutorials have to do with deck of cards? Well, factorial are commonly used in calculating probabilities. Let me show you. took five cards out of the deck, Jack Hearts, three diamonds, seven of hearts, ace of spades, ten clubs. Now we shuffle fish. What are the odds that the ace of spades is the top card on this deck? will carry the one. Come on, buddy, you can do it. Five cards, five cards. One out of five. That's right. One out of five. Nice job your it back baby. But how many different ways or permutations can these five cards be rearranged. No, no. The answer is one hundred and twenty different ways and probability is the chance of certain outcome and specific set. So in our case it's one card out of five. But permutation is how many different ways the order of these cards can be arranged and rearranged. Even though we only have five cards, they could be arranged in one hundred and twenty different ways. And if we add just two more cards now, we've got five thousand different permutations. little. Did you say five thousand. Yep. Seven factorial is five thousand forty. All right. All right. Here's what need. You did what need you to empty out by boat and refill it all the way up with vodka right to the rim. Just needs break. You know, Fishbowl Martini would make pretty good video gone to Needwood. Ok, so seven cards is over five thousand permutations. Eight cards is over forty thousand permutations and deck of 52 cards. That's fifty two factorial permutations, which is eight times ten to the sixth seventh power, which is all this. That means there are more ways to shuffle an ordinary deck of 52 cards than there are atoms on the earth. Putting it another way, if you shuffle to an ordinary deck of cards once every second, which can't do. But if you did, in order to shuffle your way into every possible combination of cards, you would be shuffling for over Novem this million years. don't know what kind of undecillion is. didn't either. had to look it up. Turns out it's trillion times. trillion times. trillion times. trillion times. trillion times trillion years. That hurts little, doesn't it? That brings us to our final topic. Big numbers. There's number so large that if you tried to imagine it, your consciousness would collapse in on itself, forming mental black hole. great. What could possibly go wrong? Our brains do not like big numbers, even if our bank accounts do, we do OK, conceptualizing hundreds and thousands and millions. But when we start thinking of numbers bigger than that, we get we get stressed at some point. Numbers stop meaning anything. They just become these theoretical imaginary stuffs. In 1940, mathematician Edward Kassner wrote book called Mathematics and the Imagination. Now, in that book, he coined term for one followed by 100 zeros or 10 to the power of hundred. He called it Google, which is just word that his nephew, Peter Kassner, being the show off, that he is then proposed an even bigger number called googolplex, which is ten to the power of Google, or one followed by Google Zeros. Well, Kassner himself called this number unfathomable. That say write googolplex is number so large that if you wrote it out in an actual notebook, your notebook would weigh more than the entire Earth, all the earth fun fact. The original Google search engine was based on sites back linking to each other. So they called the algorithm back rub. That name was clearly awful. So they decided to change it to Google because they wanted to index an unfathomable, unfathomable little Web pages. The only reason Google is spelled the way it is, is because Larry Page misspelled it when he registered the domain name. So the name of one of the biggest companies in history is actually typo, seem to be doing OK with it. Numbers get even bigger than googolplex, much bigger. In nineteen seventy one, mathematician Ronald Gramme established number as the solution to mathematical riddle. Link, link, link grammes. No, as it came to be known is so mind boggling. The human brain can't even picture it. There's sixty four steps required to obtain Graham's number, and after the first few steps the sequence contains seven point six trillion threes. don't know what happens after those few steps, but it sounds sounds awful. According to the website Physics Astronomy, if you even try to imagine Graham's number, your head would break down into mental black hole because it cannot store the information required to envisage it. think that means see, and if you think that sounds like an exaggeration, so did But John BIA's, who's mathematical physicist at UCLA, he said the mental hole description is ridiculous underestimation of how big Graham's number really is. Now, love to show you Graham's number. really would. But there actually isn't enough space in the entire universe to write down all the digits. So I'll just stick to making history by shuffling my playing cards. And remember, every time you shuffle your own deck of playing cards, you probably just made history, too. And now you know why. Thank you so much for hanging out with us today. My name is A.J. That's Hellfish. This has been the word files. What other crazy math facts are out there? Let me know in the comments section. And if you enjoyed this video, hit the like button, it really helps us out. If you haven't subscribed, please consider subscribing. If we didn't earn your subscription today, promise we'll keep making nerdy fun content until we do it until next time. Be safe, be kind and know that you are appreciated. Has anybody seen this yellow?