A clever way to estimate enormous numbers - Michael Mitchell

View the full lesson here: ed.ted.com/less...
Have you ever tried to guess how many pieces of candy there are in a jar? Or tackled a mindbender like: "How many piano tuners are there in Chicago?" Physicist Enrico Fermi was very good at problems like these -- learn how he used the power of 10 to make amazingly fast estimations of big numbers.
Lesson by Michael Mitchell, animation by Mark Phillips.

[@Ayplus]

Wow. That was amazingly accurate for just guesses . What is this black magic u call estimation?

[@brannantisdale815]

+Antoine Rashad Lel

[@snowballeclipse4991]

idk look it up

[@louiswouters71]

They judt picked one where they would end close. A lot of time you will be really far of the answer. Like one order of magnitued difference would have made an estimate of 1000 which is in my opinion really far of

[@Alvionalx]

Algrebra

[@ritwikbhandari8956]

I'm loving the energy from the 'power of 10' guy.

[@djoakeydoakey1076]

Enrico Fermi was at a pub, he asked the barman for 10 pints of beer. The barman replies, well that is an Order of Magnitude!

[@oscaar_3985]

lmao

[@NumbToons]

i see what you did there! very clever

[@kenmore01]

Or, sell him ten and give him seven and say close enough.

[@FaceofFrequency]

These TedEd's are still pretty simple, but this one was very well done and useful. Not something everyone learns in school, let alone by 4th grade

[@aspasricha]

How many Enrico Fermi's does it take to fix a lightbulb?

[@aspasricha]

Ans: 10^0

[@jeanicehoffing8935]

lol

[@myrjavi]

psyaap that is equal 1

[@aspasricha]

Thats the point.

[@uniqueusername_]

10^0

[@FootLettuce]

Obi-Wan is also a master in those Fermi problems. His overestimate of the high ground and underestimate of Anakin's power balanced out to yield a precise result of Anakin's next moves so that he could slice him off easily.

[@Alive6371]

Is he an anime character ?

[@ssjkaryuusennin]

@@Alive6371 There is a star wars anime but Obi Wan doesn't appear there

[@Alive6371]

@@ssjkaryuusennin I never watched any of the Star Wars movies. 😅

[@voodoochile4147]

3:33 Narrator: Now I know what must be thinking. Me: That guy’s gonna break those pianos? 🤷🏾‍♀️

[@EpicFishStudio]

I just love the animation style

[@gabemerritt3139]

some of it was unerving

[@OrangeC7]

my only question to the animators is why the speed of light has to be a fat person.

[@LupeSunglass]

Dat Epic Fish When the dude pointed to the paper that said 84, look at his finger.

[@dragonmanover9000]

@@OrangeC7 Because it's a big number.

[@phanibhushantholeti9446]

The best part is the video doesn't talk of miles and gallons :D

[@mancheaseskrelpher8419]

I agree.

[@mauz791]

Yes

[@nataliakurczuk7176]

Yes :-)

[@FSS666]

YEEAAAAAHHHH BOIIIII AFTERRRRR A 10^100 clicks ONE video did not have the imperial system

[@tranmanhuc6235]

True

[@kenbobca]

I like it, like it. Just a little too Fast for me.

[@KevinCummins]

Watch it again - slow it down

[@blizz3975]

I would say you need to slow it down by 10 to the power of 1 to understand it completely.

[@waywardrhythm]

I feel like the animation made it harder to follow..kind of ironic if you think ab it

[@sirmetaladon]

The constant "power of 10" advertising was quite funny. Keep it up!

[@ridheesh4765]

I have been doing this all my life without realising there was a study of it, you learn something new everyday!

[@khaled3248]

Wow! I never knew that you could tune pianos by hitting them with a tool. It's probably the new way to do it! LMAO

[@fwepbwep5752]

1:51-1:52 1 exam pill xD 😅😐😂🕶

[@claycoppinger2983]

was that a especially disturbing animation to anyone else?

[@alicetycable6107]

Yes.

[@dragonmanover9000]

Well yeah, but sometimes, even the grossest animations can be funny as well.

[@koin799]

one of the pianos is Batman. Changed your opinion didn't I?

[@hb.raafay]

an*

[@dontspikemydrink9382]

@@hb.raafay shut up

[@dulguunjargal1199]

Big respect to the person who read every phonebook in chicago to find those 81 piano tuners

[@GronTheMighty]

You can also apply the opposite principle of negative powers to easily reduce numbers that you need to memorize or add/substract in a rapid fashion, such as when figuring out how much your grocery shoppings are going to total. I.e 12, 27, 33, 16, 98, 44, 51, and 61 you reduce to 1, 2, 3, 1, 9, 4, 5, and 6, totalling 31, multiply by 10 to 310, giving a decent estimate for the actual value of 342. You can of course round up/down normally instead of forcing the round down if you want accuracy :)

[@prateektopinkatti2487]

I ain't going to a single one of those 81 piano tuners if they're gonna hit my piano with a spanner like that.

[@HappinessAWAITS]

I was so scared that guys finger was going to break when he pressed it against the phonebook D:.

[@billyspongemonkey]

This is a cool video! It would be really cool, and maybe helpful if there was an Engineering Notation video that follows this one. Now that everyone can understand the powers of ten with this video, I would like more people to know what I am talking about when I say things like: 4.8 Ghz, 12 pF and 1 k-ohms. Thanks for the video!

[@GetMeThere1]

The actual point I was making was that the proportions of pianos to residents AND proportions of tuners to pianos could well be considerably different between different cultures. The method does depend on the ability to make realistic estimates of the various proportions.

[@abdurog1122a]

Batman piano! 3:30

[@spirk314]

Thanks

[@mauz791]

Nice

[@thalespro9995]

Wow didn’t notice

[@R4Z3RHD]

This channel is amazing! please continue to enlighten me :)

[@shubhamvishwakarma8309]

Best animation ever on channel.

[@KemaTheAtheist]

Irnich D, Behrens N, Molzen H, et al. Randomised trial of acupuncture compared with conventional massage and "sham" laser acupuncture for treatment of chronic neck pain. BMJ. 2001;322:1-6.

[@Korupshenv1]

Wow......how incredibly useful and quick!

[@56independent]

i thought secondary school taught me this. until you went on about estimation. ted-ed wins again.

[@RelatedSnow8420]

0:59 I like how he said "for example" as "four exam pill".

[@0901강민재]

거대한 숫자들을 나타내기 쉽게 만드는 방법에 대하여 배워보는 시간이 되었습니다. 수학은 참 단순하면서도 메세지를 분명하게 전달하고 어디에서도 필요한 아름다운 학문인것 같습니다. 수학의 재미를 느끼는 시간이 되었습니다. 저는 이제 수학을 하러 갑니다. 좋은 시간 정말 감사합니다.

[@199NickYT]

Good lord, this animator is ridiculous...ly awesome!

[@うなな-d2e]

Wow! There are many websites that teach how to perform Fermi estimation, but this video explains why it is an efficient method!

[@brokenman4414]

but how can there be 3,000,000 people in Chicago if I'm the only person on earth

[@MsSBVideos]

+The name of a broken man You're not. I am. Wait. I am just 5/6 person. The rest of me is alien. Oh well. There are still a lot of people around.

[@brokenman4414]

+SamThe RandomG1rl Like I said, I'm the only person.

[@MsSBVideos]

+The name of a broken man There is way more persons.

[@brokenman4414]

+SamThe RandomG1rl no there isn't you're a hologram

[@TruKave]

+The name of a broken man no I'm the only person on earth ur the hologram so JUST ADMIT IT.

[@woodyeckerslyke]

Correction? Greater than *or equal to* 1?

[@Jessica-hl4mo]

it doesn't even matter, the animation were incredible

[@sqdexe]

I love that style.

[@PRICEtimeLESS]

wonderful illustration.

[@alexmihalcea6903]

Hah , "that s the power of 10",get it? Oh dear..

[@joelpaley9912]

LMAO

[@invisiblejaguar1]

Love the animation, as always :-)

[@Galloh]

If you're in a discussion with someone and you need a quick answer without having your phone with you. The discussion can be about any subject, and it can simply be for the sake of discussion, but it can also serve as a grounding for investigating business opportunities. Next that, if you're reasonably good at estimations, it'll help you verify the validity of your answers in maths, physics, chemistry and economics class. Lastly you can argue whether your search in the golden papers was complete

[@hungsangchan]

You know people actually ask that question in interviews now-a-days. The purpose of which is to test your problem solving skills and the process one goes through to come to a conclusion. Good god, I hope I get this question in my interview now and then I can just recite this video and look mad clever haha!

[@TheBelmontClan]

Enormously favorite? Is that like the collective size in reference to space particulate? Or is the enormality of it simply filling the void of it's enormous emptiness? Wow, those super giants are enormously linguistical.

[@lisafitzsimmons]

3:16 close your eyes and listen to all the sound effects

[@snail123O]

?

[@sofiamontelibano2054]

kimberly treisman that is some crazy music.

[@xjoy1163]

anyone else here cuz they wanted to know how to guess the lollies in a lolly jar?

[@zayedahmed5036]

nope

[@johngoiri7721]

+Karen Suba If you want to know the number of lollies in the jar, you can take an average of everyone else's guesses and you'll probably win

[@paulmag91]

No, because almost everyone tends to guess way to low on those things.

[@pelliqw6633]

no one was cuz we didnt know theyd mention it in the video

[@AB-rq1zt]

PaulMag periods and commas are good, but you forgot too*

[@austincathey3829]

If you like the concept of this video there is a good book that goes further into the concept of estimating to within a magnitude of 10 through a range applications- Guesstimation by Lawrence Weinstein.

[@Xylax23]

Whoa that's a slick catch

[@Abyssrian]

God I love Mark Phillips's animation.

[@tingsteph]

0:26 is nobody going to appreciate the fact that they are in the KZbin banner?

[@MilesDeep]

Great animation!

[@zelda12346]

Eh, so there was an extremely high probability that the number of piano tuners in chicago was between 10 and 1000? That interval seems a bit large to be useful.

[@gamerbro70]

Doot.

[@mindlessreader1595]

Z-Statistic 100 and 999

[@zelda12346]

Mr. Bulbasaur's Channel No, because that's an asymmetrical log interval around 10^2 when it should be symmetrical. It would have to be between 10^1.5 and 10^2.5, but then the radius is now 10^0.5 when the purported radius of the procedure is 10^1.

[@mindlessreader1595]

Z-Statistic um...

[@name_not_loading1385]

Z-Statistic actually he said there was between 10 to 100 piano turners

[@J.5.M.]

These animations! So entertaining

[@sizanogreen9900]

Great animations.

[@agarg9627]

I was writing an essay and this vid was so helpful to me. :D

[@energysage9774]

Actually acupuncture can help with pain relief, and it seems to be more statistically significant than could be explained by the placebo effect. A probable explanation for this effectiveness is given by the pain-gate theory, and endorphins almost certainly play some role as well. However, no evidence has yet to emerge suggesting that the location of the needles matters much, which practicioners do often believe (i.e. the supernatural elements of it obviously fail to meet scientific standards).

[@clarakster9510]

3:31 BATMAAAAN!

[@iamkrishradha]

Nice Observation

[@KingSiracco]

yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeea

[@Savaniel]

Because they are using that power of ten to represent every number from 100-999. They are saying that it is somewhere in that range and thus would be between 1 and 10 if they divided it by 10^2.

[@Emgurl12]

literally i watch these videos and its crazy because im learning all this stuff in chem the day these vids are realeased... crazy

[@Grezify]

The order of magnitude would still be correct even if there are as few as 317 piano tuners.

[@Dg0swe5ts]

He says "roughly ten to 10^2 pianos" hence the use of the word "approximate" @Willsirallen.

[@aldric2252]

The guy in the commercial is Billy Mays.

[@IRON9LORD]

LOVE TED VIDEOS,, MUST WACH'EM ALL MUST NOOOT SLEEEEEP

[@BluncheonMeat]

Perhaps this is useful for approximating values that do not need any level of accuracy, but for figures whose accuracy is significant, it's still necessary to round to the correct number of significant figures, even if using scientific notation. Interesting video, but a bit over-simplified in my opinion.

[@london187]

i laughed so much at the piano tuner :D Fixing like a boss :P

[@ZeroArtsMade]

Batman 3:30 lol but buy the power of 10!

[@exiledmedia]

Animated by the brilliant Mark Phillips.

[@SaceedAbul]

I'm going to start using this

[@kvell24]

Lol I did Fermi questions as one of my science Olympiad events last year... Sample question for all of u... This was on one of the tests. Excellent question BTW. How many matchsticks laid end to end would it take to reach from the earth to the Andromeda galaxy, when the earth is at a minimum distance from the galaxy? See if u can figure it out guys. I challenge thee.

[@Galloh]

Light is a physical phenomena (it's actually a combination of electricity and magnetism behaving in a specific way). The way you see the world around you is because your mind creates an image of the light going in to your eye. Blue is only blue because our brains are wired to think that. As for numbers, that's basically purely imaginative. Sure, physics' underlying mechanism involves numbers, but it isn't a real phenomena.

[@Altanthares]

By far the former. Even if the number of grains of sand is actually about 10^18 (according to University of Hawaii), there are still some several thousands stars (in the observable universe) for each grain :) Pretty cool...

[@lennoxtvthingy7408]

Well there may be as many as 10^24 stars in the observable universe, so more like a million(10^6) per grain.

[@aviralomar3760]

Please make a video on calculus!

[@bbrabant]

THAT'S NOT HOW YOU TUNE PIANOS! *internally freaking out*

[@ykcul95]

AWESOME.

[@zotzot5]

3:31 batman piano!

[@leontinetenhovejansen6239]

thx you helped me really

[@Altanthares]

Indeed. Moreover, to check them ALL would be rather improbable (ok, "definitely impossible" is more appropriate). Just the sheer distance of the vast majority of those stars is such that we can't possibly distinguish them individually: we just see the galaxies that contain them. Nevertheless, even the most pessimistic guesses on the Drake equation are very happy with a number of "candidates" much much lower than the total...

[@FightClubStellingen]

you are awesome, nothing more. Learn to deal with it!

[@igorsoarez]

Unmentioned assumption that on average, pianos are tuned once per year.

[@rev.davemoorman3883]

Assumption tuners tune 2 pianos a week?

[@gordontaylor2815]

Igor Soarez If you listen to the video carefully, they assume a "couple hundred" pianos tuned per tuner per year and use 100 as the closest power of ten in their estimate. This is reasonable considering how complicated and time-consuming the task is and how many working days there are in a year (even assuming one a day, that's only 250 or so pianos possible in a year). It doesn't really matter how often a piano goes into be tuned, a piano tuner can only do so many in a year, and that's what they use for the estimate.

[@kucasmukas7942]

+Gordon Taylor That'd make the number of pianos completely irrelevant. I guess you could with the magnitude approximation with this one too, although it was omitted. 10^1 times per year is way too often and 10^-1 would make one pretty much useless, so 10^0 sems like a good guess.

[@govindagovindaji4662]

How do you know which power of 10 to use at any given time in your problem?

[@richardsantalone9380]

I lost my mind when I saw that "Power of 10" advertisement

[@MariHalo]

I don’t understand this and I have to do 10 questions by tommorow. Save me lord.

[@AnantMall]

mark philips ... atleast search his name to say thank you ! he really is too good !

[@cheeseburgermonkey7104]

3:59 81 is actually 9^2!

[@elitheiceman5608]

So what's the point?

[@TheJJ65]

God I love the crazy scientist Fermi

[@6SLeGM]

2.705 million people live in Chicago.

[@matthewwalker4521]

Wow very helpful and interesting

[@melancholiac]

A pretty good approximation that I never heard even once at school, college or in a long engineering career is this: The Speed of Light, as near as makes no difference, is a Million Times the Speed of Sound. You're welcome 🙂

[@TeagueChrystie]

Where'd you get 81?

[@FahadSiddiqui1]

This is a very clever way to teach.

[@freebirdwithnest1012]

powerful video!

[@Tamizushi]

Hey I thought the video would be about being able to visual enormous numbers, something I'd like to be able to do. Like I undestand that 1000,000,000,000 is 100 times smaller than 100,000,000,000,000 but without comparing them together they are both mean basically the same thing in my mind: more than I can fathom.

[@ajezaseden]

3:31 a hidden BATpiano :D

[@martinb.3997]

EstimationA+EstimationB+(EstimationC+EstimationD)= EstimationE EstimationE~=Result I am beggining to think that humanity is waay more predictable than we think

[@terrariaman8454]

How many oranges does it take to screw in a light-bulb? ANSWER: 617.

[@iceberriz7105]

Terraria Man We need to take into account cost, volume, energy production, etc. I'd say over 9000

[@ajiprnk4821]

I don't really understand what you mean? And the using the video"s way of estimation Will always be a power of 10

[@Angela-ou5wb]

This is pretty cool, I just dont understand how he can estimate that around 10 to the 6th power people live in chicago

[@Markd315]

Angela Zheng Well, it's got to be a couple million, right? It's a big city, and small cities have several hundred thousand,

[@pawankumar-zr1rx]

Yes 10^5 is 1 mil and 10^6 is 10 mil... Assuming closer to 10 million 10^6, as it could be 2,3,4 ...>1 mil. The closest approximate to number line 1mil to 10 mil is to far end which is 10^6. Hence 10^6

[@dogbreedsareamyth9409]

pawan kumar No, 10^6 is 1 mil

[@Toleich]

Awesome!

[@ABDULRAHMAN-ov4uj]

Mind =blown

[@matthannigan78]

But the whole point is that they're on the same magnitude. 3 million is, in fact, 3 times more than 1 million, but when using other numbers on other magnitudes, like those that are on the magnitudes of 10^2, 10^4 and 10^-2, the difference between 1 million and 3 million (3 multiples) is way less than the difference between 10^6 and 10^2 (4 orders of magnitude, or 10,000 multiples).

[@tylerolsen1643]

Idea to make this much easier: drop many nukes on chicago and then say there are no piano tunners

[@voliverak47]

Pretty cool.

[@rishabashok3388]

1:15 How to guess accurately how many m&ms are in a jar 1. Eat all the m&ms in the jar 2. Put the jar back and say zero

[@BallinAndCantGetUp15]

HI BILLY MAYES HERE WITH AN AMAZING NEW PRODUCT!!! POWER OF T E N