One Weird Math Trick to Estimate ANYTHING

today's episode is sponsored by kiwico but more on what's inside these boxes in just a bit hint it's science in case you didn't know who i was which you might not on july 16 1945 physicist enrico fermi was standing about 10 miles away from what would become ground zero for the world's first atomic explosion but instead of simply observing the blast that he personally helped bring into being during the manhattan project the scientists that he was he was tearing up and dropping small sheets of paper before during and after the explosion once the blast wave reached him about 40 seconds after detonation he used how these pieces of paper fell through the air to estimate that the blast yield for the nuclear bomb the trinity test was about 10 kilotons of tnt equivalent it turned out later to be calculated as 20 kilotons of tnt he was that close just by looking at how pieces of paper move through the air enrico fermi had a legendary ability for estimating very complicated phenomena for almost no data at all he became so good at this in fact that the estimate of this kind became the fermi estimate and i'm going to show you how to do it today to estimate nearly anything although the air is moving around at about two kph in here by the way now entering the facility today's program will be all about exercising your brain and thinking about how to think better so if you want to follow along with me feel free to pause the video at any time grab a sheet of paper and a calculator preferably a ti-89 titanium we begin with the mathematical basis for fermi's legendary estimating ability dimensional analysis dimensional analysis is a way of relating units to one another to quickly convert one unit to another so an easy example of this would be to ask you how many seconds are in a year this is something that's difficult to know off the top of your head but this is where we apply our analysis we begin with a number that we know like there are 365 days in a year right well we also know relating the units that there are 24 hours in a day and 60 minutes in an hour and 60 seconds in a minute now as long as all the units cancel out top and bottom and we're only left with the unit that we want then we can multiply across the top divide across the bottom and bam we get the seconds in a year a little over 31 and a half million this seems like a simple process and it is that's the power of it but we can do something a lot more difficult than just seconds in a year why don't we try something a bit more worthy of our newfound abilities how about something with your hair that's definitely worthy baby a few years ago when i was still trapped in a formless emotionless void one of you nerds asked me a question that i couldn't possibly know off the top of my head about the top of my head you asked me would all of my golden locks laid end to end reach the moon well it sounds like a science effect you may have heard of before about human beings but it's perfect for a fermi estimation so let's apply the fermi estimation process the first thing that we're going to do is identify and break down the problem what do we need to know to make a good guess well we need to guess the distance of the moon the number of hairs on my head and the average length of those hairs the next thing that we're going to do is just throw out some numbers and dare to be imprecise here because over and under estimates tend to cancel out that's the real secret of this process how far away is the moon is it one kilometer away no is it a million kilometers away no well it's hard to say where we should land if we don't apply the third step which is bounding the problem use figures and numbers that you have some confidence to start with for example i know that space starts a hundred kilometers above your head and that the sun from earth is about 150 million kilometers away so for the moon order of magnitude i'm gonna say it's a hundred thousand kilometers away to start and for the number of hairs on my head i'm gonna say about ten thousand because one thousand sounds like too few and a hundred thousand sounds like way too many and finally for the length of my hair i know it's about the length of my forearm which is a third of a meter or one foot now it's time for the dimensional analysis i'm guessing there are ten thousand hairs on my head and each one of those hairs is point three meters long one moon distance for us as a unit is going to be a hundred thousand kilometers and if we multiply and divide cancel out the units at a glance you can tell that all my glorious hair laid end to end is not gonna make it to the moon now three percent to the moon is a long way but we'd estimate based on this dimensional analysis that my hair no human's hair laid end to end would never reach the moon even those weird humans that play guitar outside of whole foods in birkenstocks in 2021 some reason so we have our fermi estimate but it doesn't stop there the final step in the process is a sanity check does this number make sense with everything else we know about the world well again like i said this hair end-to-end fact sounds like other sciency facts you may have heard of like how long all your blood vessels would be laid end to end and then you would definitely die but i think you have way more blood vessels in your body than you do have hairs on your head so i think it being a lot less than something like that crazy distance makes sense so arya could you do the final calculation supercomputers are really fast you see we came up with a value that was within 50 percent of the true value we were off yes but we were so close that we still answered the question completely correctly this is true mathematical power if you follow these steps with rigor you should be able to estimate things that you have no business knowing off the top of your head and i really want to prove this to you today let's try something a lot more difficult growing up my favorite animal had to be the great white shark so here's the fermi problem for me how many great white sharks are swimming off the coast of california right now that sounds nearly impossible to guesstimate without looking anything up right well witness the full power of a operational fermi estimate as we use educated guesses to hopefully get within proximity of the correct answer now being my favorite animal i do know some facts about great whites but this is going to be difficult even for me pay attention to how i follow our fermi steps i know off the top of my head that your chances of getting attacked by a shark are about 1 in 4 million if we compare that number to the 7 billion people in the world or thereabouts that should give us a ballpark number of yearly shark attacks i'm now gonna guess that the minority of attacks are fatal maybe five out of every one hundred i also know that just three shark species make up the majority of fatal attacks so i'll say that only one out of every three fatal attacks per year are by great whites but not every great white will commit a fatal attack this number has to be small based on the total population so i will further say that only one out of every 100 great white sharks in its lifetime has a chance of killing anyone finally i can only think of three main habitats for great white sharks off the top of my head hawaii south africa and the coast of california so i'll say that of all the great whites we ended up with in our dimensional analysis only one out of every three of them are off of the coast of california swimming and eating seals right now are these weird numbers to use that i'm almost pulling out of nowhere yes could we be way off high or low yes but i'm trusting the method now after all that admittedly extreme guesstimation it would be pretty impressive if we could get close to the actual number of great white sharks swimming off the coast of california right now wouldn't it okay so i did not ask arya to calculate anything until just a few minutes before she turned the cameras on okay so arya would you do the honors okay this is our fermi estimate but now for a sanity check how close did we get arya according to an estimate of white sharks off central california the population of great white sharks off the coast of california is estimated to be between 300 and 400 individuals look at that we started with odds in the millions multiplied it by numbers in the billions and then started pulling stuff out of our hats and this is how close we came within a factor of three of a very esoteric number the current population of great white sharks swimming off the coast of california right now come on you gotta be impressed by that unless you're a seal that's not good news this is the real advantage of the fermi estimate it's so useful that i think all of you should learn it and practice it and i believe in this so much that i'm gonna do something i've never done here at the facility i'm gonna work through a number of these problems with you in real time with no fancy editing or camera tricks to edit out my mistakes or if i get something totally wrong are you sure that's a good idea well that's a good thing about science aria it works whether or not you believe in it i didn't steal that from an inspirational quote that's been shut up as i said at the top of the video today's episode is sponsored by kiwiko kiwiko is a perfect sponsor for today's episode about mathematical thinking because it is a monthly subscription box with the explicit purpose of getting kids and families excited about practicing the principles of steam science technology engineering arts and math each kiwi co box comes with everything that you need to complete the month's puzzle or brain teaser or build or make no running to the store to buy extra supplies like duct tape what aisle is that even in anymore and the mind and problem solving skills you need to complete the context of each box are perfect for engendering the kind of skills in kids and young people that they will need to solve today's problems tomorrow kiwiko also has families and availability in mind it ships to now more than 40 countries and provides hours of science entertainment each month no matter if you are 8 108 or immortal like me if you want to try kiwi co like i did you can go down into the description of this video or go to kiwico.com kyle to get 50 off any first box of your choice it's the perfect gift or monthly activity to get your mental gears uh spinning and i mean look i just i made an air hockey table right on my desk here it's perfect especially if you're doing fermi estimations all day like yours truly let's get back to that okay so to prove the power of the fermi estimate method i had arya write down some fermi problems on some sheets of paper that i used to estimate the strength of a nuclear explosion and keep in mind i have not seen these or thought about these beforehand i'm gonna try to do them in real time here with you without any fancy editing to hide all my mistakes and whatnot i might cut here and there to save you time but we're gonna do this we're gonna we're gonna arya if you could uh hand me the sheets of paper please okay let's get started thanks uh you can go if if you never cut your hair in your whole life and it grew continuously how long would it be okay so another hair question what we do uh start from the place of confidence right with our numbers as we're throwing out numbers right so i know approximately that hair grows what five millimeters uh weak does that sound right so five millimeters a week then we would start our dimensional analysis so if we start five millimeters a week we know that there are 52 weeks oh that's the wrong i didn't 52 weeks in a one year and the average person uh lived 72 years in one life oh i mess it up again there's 52 weeks in one year [Laughter] and it's not not pretty when you when you're just doing it like this uh 52 weeks in one year and there's about 72 years in one life time so in how long will your hair get perm in in millimeters in one whole lifetime well if we multiply these things to get my calculators out of batteries that's it's perfect that's perfect that this is uh so in so we have five milliliters millimeters times 52 weeks times 72 is equals 18 720 millimeters which if we divide by a thousand to get meters we have 18.72 meters which is roughly a lot of feet so i'm going to say that it's around 18 meters if you let it go next question we got from arya is how many points were scored in the nba total last season well if you want to know anything about sports you came to the right guy so uh how many so okay so total number of points let's throw out some numbers and let's bound the question right i know there's not five points scored in an nba game i also know there's never 200 points scored in nba game i think uh it's around 100 something like that and each team is gonna score around a hundred again if we're going order a magnitude it's not ten it's not a thousand let's say a hundred so each team is gonna score combined 200 points per game total right so 200 points if we're estimating 100 points per team 200 points per game now how many games are in an nba season i have no idea is it is it dumb like baseball so that the win percentages don't really mean anything uh i'm gonna say a hundred it's somewhere between like 90 and 200 right again we're bounding here so i'm going to say that there are 100 games per season right and now we cross out games and we get points per season points per season but is that total yeah right twenty thousand twenty 000 points per season okay come on arya that was an easy one right how many dump trucks would it take to haul away all of mount everest that one is significantly harder we're humans we have technology why don't i just the fermi estimate will be for something that'd be much harder the dump trucks uh we know we can calculate the volume of everest everest has been measured all over the place so um i'm gonna look up the volume of everest no this isn't cheating this is using what we have okay the volume of everest is 2.1 times 10 to the 12th cubic feet okay so 2.1 trillion cubic feet how big is a dump truck well i've i've stood next to a large dump truck before so i'm gonna say that okay so i've stood next to a dump truck dump trucks are pretty tall i'm gonna say they're twice my height so and and and width-wise lengthwise they're they're twice let's go three times my my body length because they're big trucks and then twice my body length for the width okay i'm just i'm i'm estimating a very complicated thing just based on how big that i remember it being next to me sounds like not a great method but that's the power of fermi so i'm going to say that one truck can hold a volume that is equivalent to what i just said so my body length i'm going to go the height is 6 feet times 18 feet times 12 feet for the volume of the truck and so this is going to equal cubic feet so that cubic feet cubic feet will cancel out there and i will get a value that will be i'll get a value for the number of trucks that we need to haul away all of mount everest if you ever wanted to do that because you're a crazy person i'm not slow at typing you are you get 1.6 billion dump trucks wait a second something about this basketball estimation has to be off 20 000 points sounds like it's way too few considering that someone like stephen curry is scoring 2 000 points in a single season i didn't have to look that up so instead why don't i i'm going to go back to the drawing board a little bit so instead of 200 points per game for both teams i think that's an incorrect unit to have instead i'm going to go 100 points per game per team yeah so each team is scoring 100 points every single game i'm still estimating that there's a hundred games in a season because i have no i don't know how many there are and i know that there are 32 teams so now if i multiply 32 times 100 times 100 that's 320 000 points per season which is a lot but i think or at least hopefully it will be a lot closer to whatever the true number is okay did you follow along with me that all makes sense how did our fermi estimation go points in total number of points uh in an nba season how long your hair would be if you never ever cut it and it grew continuously how many dump trucks you need to haul away all of mount everest okay so if everything i've said up until this point is true then we're getting pretty close to some accurate answers that you wouldn't know off the top of your head so let's see how we did okay so how do we do i did not look up anything i have not calculated anything yet so let's see see that's not so bad we might be off by a factor of two or five or ten somewhere but usually with these kinds of estimates we don't need to be exactly right in order to say something accurate about a situation or to make a decision and move forward clearly this is an incredibly powerful way of thinking but it does have its pitfalls if you're not at least starting from some place of confidence some fact or figure that you know you might be way off in modeling the situation and up and down over and underestimates won't cancel out like they're supposed to enrico fermi was so good at this because he was like a genius on the manhattan project and stuff so he had a lot of places of confidence he could start from but as long as you keep all that in mind clearly the the advantages are just undeniable so get out there and get guesstimating until next time now exiting the facility thank you so much to the very nerdy staff at the facility for their direct and substantial support in the creation of this here video today especially i want to recognize research assistant cody peden and visiting scholar jackie gatt if you want to join the facility if you want to drape on a silky white lab coat get behind the scenes photos join my discord talk every day with me get private members only live streams with yours truly not like that you can go to patreon.com kyle hill and join the facility today if you support us just enough get your name on aria here each and every week lucky you and as you can see there's literally hundreds and hundreds of you so i have no idea how i'm going to pass the if you really like fermi estimates which are very fun to work through some are impossible to look up but it's always a good thought experiment and brain exercise if you really want to try some more i will post a pdf of like a hundred extra for me problems that you can try with a loan or with your family or with your kids i'll post them in the comments below get calculating but only if you have a ti 89 titanium texas instruments sponsor us thanks for watching i mean you can have any calculator you want i don't care

Channel: Kyle Hill

Views: 341,929

Rating: 4.9602113 out of 5

Keywords: because science, engineering, kyle hill, learning, math, physics, science, stem, the facility, enrico fermi, fermi estimate, fermi problem, math trick, math tricks, practice problems, guesstimate, approximate, trinity test, because science lightsaber, because science chernobyl

Id: INlPbfBGPtw

Length: 22min 52sec (1372 seconds)

Published: Sat May 29 2021