The Odd Number Rule

hey vsauce michael here why though why are any of us here what's the purpose what does it all mean well sometimes if we listen closely enough when we ask why we can hear an answer and it's another question why why what our journey begins here checking the rulebook but you won't find anything in there it says a dog can't play he's right ain't no rule said the dog can't play basketball is that true is there really no rule against a dog playing middle school basketball vsauce magic 8 ball is there really no rule against a dog playing basketball the answer is yes or is it we have begun the actor who played airbud buddy the dog passed away in 1998 at the age of nine now take a look at this let's talk about world war one on june 28 1914 franz ferdinand the heir to the throne of austria-hungary and his wife sophie were assassinated in sarajevo while riding in a car the car's license plate was a iii iii118 they were killed by gavrilo princip who said during his trial that he wanted the unification of all hugo slavs free from austria the event sparked a series of escalations in europe the july crisis which ultimately caused world war one a war that ended on armistice day november 11 1918 pretty odd huh a spooky coincidence if you will but look odd things happen all the time oddness is all around us especially in the form of odd numbers the grip they have on our reality is revealed when we release our grip notice anything strange under the influence of gravity things move in an odd way if something starts moving because of gravity after say one second it will have traveled some distance now interestingly during the next second the distance it will travel will be three times as far as it moved during the first second during the third second it will travel five times as far then seven times then nine times eleven thirteen fifteen we used seconds but it doesn't matter what time interval you use you will always find this pattern the odd number rule hiding right there within the very phenomenon that keeps us on earth are the odd numbers more like god numbers right is the odd number rule the face of the universe looking back at us well here is something that galileo wrote philosophy is written in this grand book i mean the universe which stands continuously open to our gaze but it cannot be understood unless one first learns to comprehend the language in which it is written it is written in the language of mathematics and its characters are triangles circles and other geometric figures without which it is humanly impossible to understand a single word of it without these one is wandering about in a dark labyrinth before this pattern in the grand book of the universe was read and appreciated people wondered why things fell maybe stuff just has a desire to be in its own proper place right rocks with the earth fire with the air that makes sense right it was fun to imagine causes and write our own stories but underneath our desire for explanations a story was already being told one that is written in the language of mathematics measure and relation now many of these stories are being told all around us all the time one on top of each other but if we can look past those disturbances each isolated event is narrating a quiet simple story not of why the universe is but of what the universe is galileo recognized what this pattern spelled mathematically it spells hello i am speeding up at a constant rate and that was huge all this time for millennia we had been wondering about the causes of gravity its cosmic purpose why it existed but now here was someone saying yeah yeah cool but like what does it do it makes things fall great well what does that mean what does it mean to fall fall how now the human mind alone couldn't answer that but the universe was telling us we just had to speak its language and read it this is i am gaining velocity at a constant rate spelled with odd numbers how well what's an odd number the concept of oddness comes from the observation that sometimes when you have a bunch of things everything you have can be paired up but sometimes that can't happen now when it's possible when you can pair everything up that you have it is said that the number of things you have is even if you can't do that then the number of things you have is odd now what this means is that the number of objects in an even group is equal to 2 times n where n is just the number of whole pairs that you have so n is any whole number n could be for example 50 giving us the even number of 100 which is also the number of legs centipedes have or is it centa 100 peed feet having 100 legs is right there in the name but it's only approximate centipedes have been observed to have anywhere from 30 to 345 legs now 100 falls pretty nicely in that range but every pair of legs on a centipede is attached to a body segment which means that in order to have 100 legs a centipede would need to have 50 body segments but not a single species of centipede has an even number of body segments 50 segments is nowhere to be found in the library of centipede genomes so while centipedes on average have a number of legs quite close to 100 they never naturally have exactly 100 point is 2n is the mathematical way to spell even if i add just one more thing the amount i have is no longer even it's odd if i add yet another thing i've added another pair and has gone up by one and the number is even again this means that an even number plus just one more will always be odd now that we know how to mathematically spell odd and even we can move on to moving if you and me hugged well that would be wonderful we would both get so much out of it but if during the hug you suddenly ran away from me while yelling i'm leaving you at a velocity of two meters per second well i would be devastated but i would know that deep down you still cared for me because you told me your velocity and if i know your velocity i can know just how far away you are from me at all times all i have to do is take your velocity and multiply it by the number of seconds that have elapsed since you left now take a look at what a graph of your velocity would look like here we have velocity in meters away from me per second and we have time in seconds since the hug ended now if your velocity is two meters per second and that persists then here's a graph of your velocity but look at this after a number of seconds have elapsed like after one second the distance you are away is just the rate times the time elapsed two times one well that also happens to be the area of the rectangle bounded by a line coming up from the time your velocity graph and our axes well that's pretty convenient after two seconds you are two times two four meters away from me which is also the area of this shape we've created after three seconds you are three times two one two three four five six meters away it's always the area well that's pretty convenient but let's change up the story what if we hugged and it was great i mean just almost not even a hug like something new is being invented here but then during that you suddenly leave you run away from me and while you run you yell i am leaving you at an ever-changing velocity well i would say you know what that is a lot less helpful now let's say that this changing velocity you have that i don't know happens to be an acceleration of two meters per second per second what does that mean well that means that your velocity is getting bigger by two meters per second for every second that you run it would look like this on a graph you begin hugging me with no velocity and then one second later your velocity is two meters per second larger so two larger than zero is two that's your velocity after one second after two seconds your velocity is two larger still so four and then six your velocity graph would look something like this but now here's a question if you're moving like this is the distance you are away from me at any given time still just the area of the shape bounded it's harder to see that because you don't maintain any single velocity for any amount of time your velocity is always changing so we don't have nice rectangles but we can see that it is true by putting ourselves in my shoes abandoned alone i don't even know your emotion i don't even know how you're accelerating it's very scary but i can decide to take matters into my own hands and measure your velocity as often as i like let's say that i measure it just once i measure it after let's say two seconds all right wonderful now the question i want to answer is how far away you are after three seconds all right so i have this measurement i know that you were traveling at four meters per second well i mean look if you're going four meters per second for one second then that's a rectangle like this and it's got an area of four um but you're not four meters away are you you're a lot further than that because you weren't traveling four meters per second for this entire second you were at all times actually traveling a bit faster and i'm totally forgetting all the distance you covered before my measurement which is not zero okay so clearly i need to measure your velocity more frequently so let's say that i measure your velocity twice during the three seconds i'm curious about let's say i measure it after one second and then after two seconds well now i can imagine rectangles here this one is two by one so it has an area of two this one is four by one so it has an area of four two plus four is six but you're a lot more than six meters away as well because you weren't traveling two meters per second this entire time you were actually speeding up covering more and more distance i'm totally forgetting all the distance you covered over here basically this method will always leave me short but the more frequently i check your velocity the better things get take a look at this oh yeah oh wow as you can see the more frequently i check your velocity the closer my calculation gets to being based off of what you really did your actual motion but also the more frequently i check your velocity the closer the combined area of all of my rectangles gets to simply being equal to the actual area bounded by your velocity curve which means that the area under your velocity curve even when your curve is like this is still totally the distance you are away from me now let's take this knowledge and apply it to the odd number rule before people knew how things fell there were some pretty good guesses for example if the reason things fall is that they have within them a desire to be in their own proper place uh in this example the table well then maybe the closer this object gets to the table the more excited it is to be there and the faster it goes in which case its velocity would change over time like this getting steeper and steeper and steeper but galileo didn't think that he believed that when objects fell their velocities increased at a constant rate so graphed like this their velocity would just follow a straight line let's draw a straight line beautiful now let's divide this graph up into strips of equal time perfect all right now as we know the areas of the shapes we have bounded here are the distances traveled during their respective time intervals so what's the area of our first shape here a little triangle well we don't know what it is we don't have any um actual markings here on our axes but that's fine it doesn't really matter we'll just call this one so in the first second or the first time interval our object traveled a distance of one unit of space perfect now how far did our object travel during the second time interval well that distance will be equal to that area well what is this area well one thing we can do to make this easier is to divide the shape like this now we have two shapes a triangle and a rectangle this triangle has the exact same area as our initial triangle that's because they are congruent triangles they both have the same base length and because this velocity line has a constant slope it rises the same amount per time elapsed all the time so their heights are the same and they're both right triangles their areas are the same so the area of this space is the area of that triangle plus the area of this rectangle what is the area of this rectangle well one thing we can do is divide the rectangle in half with a diagonal like this and look what we've created this triangle has the exact same area as our initial triangle it has the same height it has the same base they're both right angles and look the same goes for this one it's a right triangle its base is the same as this space its height is the same as this one's height gosh this is just the area of the initial triangle but twice so we have two of them and we have two of them one time okay perfect now let's move on to finding the area of that shape once again i can divide this shape like that and now i have a triangle which as we know has the same area as our initial triangle right here so we have that area one and then we also have look at that two rectangles which as we know we can divide in half like this giving us now four triangles equal in area to the initial one so what we've done is we've taken the initial area and we have doubled it uh well once and then twice so two times now as we continue doing this we find that we're always adding one more of our original areas and then we're always doubling that original area one more time here we've doubled it one two three times doubled three times we'll look at this pattern right here we can think of one as being equal to two times zero plus one can't we well these numbers are whole numbers and they're just going up by one zero one two three this is all of the general form two n plus 1. that is how you mathematically spell odd so the odd number rule is not some kind of magical coincidence it's just what happens when an object's velocity increases at a constant rate the answer was right there in front of us all along written in the mathematical language of the universe the universe also contains colorado one of its best rectangles or is it let's find out after a quick word from our sponsor us hi i'm michael stevens are you a person well then get out of here go poop or something i only want to talk to your brain okay so brains here's my message to you treat yourself touch more than just my voice become a supporter of the vsauce curiosity box the subscription for thinkers it comes to your door every three months full of stuff that we have made and things that we love i'm talking books shirts viral physics toys puzzles projects you name it its mission is to be good for brains so we give a portion of all proceeds from it directly to alzheimer's research and it makes our new inquisitive fellowship possible a program that literally just gives money and equipment and assistance to educational youtubers so they can worry less about monetization and the algorithm and more about just making the kind of content they want to make and that this world needs this year's inaugural fellows are fantastic 12 tone jordan herod up and adam and jabril you should definitely subscribe to them continue feeding yourself right join the curiosity box today welcome back now colorado looks like a rectangle a shape with four sides that all meet at the same angle but colorado doesn't have four sides it has 697 making it not a rectangle but instead a hexa hecta india contact heptagon and this was all by mistake the united states congress initially defined colorado as a geospherical rectangle the space bounded by two lines of latitude and two lines of longitude in the 19th century surveyors set out to demarcate its shape to actually mark it on the ground and they did a phenomenal job with the tools that they had but mistakes were made some were large enough that you can spot them on many common maps of the state in 1925 the us supreme court ruled that the borders as surveyed were the correct ones and would legally stand as the official recognized edges of the state not the originally intended theoretically pure geospherical rectangle thus ending the shaping of colorado that began with lines drawn by the compromise of 1850 18 we have arrived article 18 section 5 paragraph 0 of the washington interscholastic activities association 1996-97 constitution the set of rules airbud would have been subject to at the time and place of the movie states that in order to participate in an interscholastic athletic activity like basketball a student must be a quote regular member of the school defined as someone enrolled half time or more the section does refer to rcw 28a 225010 a list of approved exceptions but not one of these was considered in the case of airbud had they been it would have been discovered quite quickly that airbud the dog qualified under absolutely none of them there is no rule that specifically states a dog cannot play basketball but there are and were rules that said that this dog airbud should not have been allowed to play basketball and as always thanks for [Music] watching

Channel: Vsauce

Views: 2,815,041

Rating: 4.9271369 out of 5

Keywords:

Id: U6VBV4QUMu0

Length: 22min 7sec (1327 seconds)

Published: Wed Jul 29 2020

Reddit Comments

[u/Sipstaff]

You truly never know what's going to happen next in a Vsauce video. It's like riding a rollercoaster in the dark.

[u/SpiderInTheDrain]

I hope the "Let's talk about WW1" with the somber atmospheric sound will become a meme. I bursted out laughing at that part

[u/wooahstinky]

HES BACK

[u/Interesting-Current]

Vsauce videos are some of the best videos on yt. I love how he goes on the biggest tangents lmao

[u/Kaesetorte]

Hillariously convoluted intro, but it felt like he was reaaally taking his time with that graph.

[u/konydanza]

That intro has some meme potential

outlandish clip plays on tv
Michael: pauses tv “Is that true?”

[u/MysticPing]

He seems legitimately insane

[u/RustyShackleford916]

Man that dude is coked the fuck out.

[u/charmibarmie]

spoilers

The whole video leads over to why Airbud shouldn’t have played basketball

beautiful