One Weird Math Trick Estimates ANYTHING (Fermi problems)

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There once was a scientist who was SO GOOD at estimating complicated questions from almost no information that they named this style of problem after him.
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[@pirateadam3686]

Police officer: Sir, do you know how fast you were going? Me: *Inhales*...

[@berman00]

I don't know for sure, but my guess is about one half a moon distance per shark attack

[@erinkarp6317]

But officer, speed is relative!

[@andrasbiro3007]

I'm reasonably sure I didn't break the sound barrier.

[@Z31Turbo]

@@berman00 So I calculated that at about 820mph! You were going pretty damn fast! Shark attacks have really increased a lot in the last 20 years, apparently.

[@vincentochs637]

This made me laugh so hard I almost peed my pants

[@Jason-ue7gi]

As a middle school science teacher, I use fermi estimates ALL THE TIME to answer crazy questions from my students that I have no way of 100% correctly answering on the fly

[@HauntaskhanHYPNOSIS]

I think all my science teachers did the same. Lol Edit) Although I had a physics teacher that was too comfortable with the phrase "That's impossible" Real dream crusher. Lol

[@BigDaddyWes]

@@HauntaskhanHYPNOSIS That's when you say, "It's impossible for you, but not Fermi."

[@gonzalodasilva1229]

@@BigDaddyWes great pun sir

[@lunartransport5461]

So you lie to your students regularly... nice

[@Steampuke]

@@lunartransport5461 what ?

[@lucafiore6275]

Thanks Kyle, now I can get every question on my math tests almost right.

[@maoman4855]

"I have approximate knowledge of many things"

[@zzz_zzz_ZZZ_zzz_ZZZ_ZZZ_Z_z-ZZ]

@@maoman4855 would this count as a shitty superpower?

[@tristanmurphy7337]

@@zzz_zzz_ZZZ_zzz_ZZZ_ZZZ_Z_z-ZZ yoooo definitely should be

[@zzz_zzz_ZZZ_zzz_ZZZ_ZZZ_Z_z-ZZ]

Actually on a second thought this can be a god-tier superpower on par with omniscience to a lesser degree though. So, in theory you can predict anything with this power. Assuming your approximation has a constant error you can always just correct it by using the constant. Stock market here I come

[@richunclejoey2249]

@@zzz_zzz_ZZZ_zzz_ZZZ_ZZZ_Z_z-ZZ that's why I'm watching this..find a constant deviation, program an EA and forward test it on commodities trading..lol

[@enginerd1985]

I love how the Drake equation is simply a Fermi estimate, jumbo sized.

[@mlembrant]

i use this method to estimate how much dough will be needed for tomorrow so i can make enough pizza that customers will order that day ^^

[@borttorbbq2556]

@@mlembrant I do it too for all prep

[@borttorbbq2556]

Also yes it basically is.

[@maxmccann5323]

Yeah same, whatever that means

[@-MrFozzy-]

The Drake equation is just a totally made up guess…it’s barely an equation. His guess just had great PR. Evidence?! 1 million intelligent civilisations in our universe (or galaxy) I forget……but, it could be none, it could be five…

[@THE_KIRYU]

"what's 9+10?" Enrico Fermi: "21"

[@werebison]

Three statisticians go hunting. The first one takes a shot, missing 1m to the left. The second misses his shot 1m to the right. They all high five and go home.

[@ImieNazwiskoOK]

*29

[@Joseph125]

Eh, it's the right order of magnitude. Close enough. Once you've seen lecturers estimate pi as 1 and 10 in the same lecture, anything is reasonable.

[@Nightriser271828]

@@Joseph125 engineers, amirite?

[@The_Viktor_Reznov]

@@Joseph125 π = √g = e = 3

[@mattgunnell9416]

I remember doing these kinds of exercises in school. My dad calls these SWAGs: Scientific Wild A$$ Guesses

[@MaryAnnNytowl]

LMAO, that is what MY dad called them, waaaaaay back when I was a little tyke, about 50 years ago! He was an engineer/radio man for decades, along with helping to design the first radar systems for the downtown KCMO airport, about 7 decades ago. He had a solid understanding of sciences and math, and often used this method, literally calling it a SWAG! Thanks for the walk down memory lane! 😊

[@matthewcox7985]

Show your SWAG! 🤣

[@mattgunnell9416]

@@MaryAnnNytowl you're welcome! 😀

[@Lambda_Ovine]

I doubt any dad to be that cool

[@geordannik]

That's actually a proper phrase! Wikipedia it lol

[@nightthought2497]

The best part of a Fermi estimation is that once you've done it, you have an incentive to check your work, providing yourself with even more points of confidence.

[@goldenoreo9171]

That "Texas Instruments, sponsor us" at the end made me laugh my ass off. I'm sitting at work, on break, at a Texas Instruments facility in TX at this very moment

[@Xadov]

Please sponsor him

[@Skelterbane69]

So.... Is that a yes?

[@maoman4855]

And I immediately hopped up to grab my TI-89 Titanium! ...then hopped up again to search for my TI-82 which was buried in my under-bed drawer ...then hopped up again to put batteries in both of them because I haven't touched either in almost a decade. But I knew where they were!

[@DialecticRed]

​@@XadovThey're likely just an employee, who does not have the power to do that.

[@Siansonea]

"Is that a firm estimate?" "No, it's a Fermi estimate." "Isn't that what I just asked?"

[@dinamosflams]

"almost"

[@madkirk7431]

@@dinamosflams *well yes but actually no*

[@boio_]

@@dinamosflams lmfao

[@anchovybushwack472]

Three replies in and I already love this thread

[@Random_Nobody_Official]

@@anchovybushwack472 make that four.

[@niamhythedegen]

"A few years ago when I was trapped in a formless, emotionless void-". Ah, so working on Because Science

[@stelmaria8991]

Yes, that's the point

[@AxxLAfriku]

AAAAAAHHHHH!!!! PAAAAAIIIINNNN!!!!!! I broke my hand yesterday because of the hate comments I get all the time. I was so angry that I punched a hole in my computer. Please don't hate me, dear mera

[@niamhythedegen]

I have ascended, I've received the fabled AxxL reply

[@AxxLAfriku]

@@niamhythedegen *AxxL

[@niamhythedegen]

@@AxxLAfriku ah yes of course, how foolish of me

[@WitchVulgar]

Title: How to estimate anything Me: All non-infinity numbers round to zero

[@IceMetalPunk]

"When you consider the number of particles in the universe, or the age of the universe at the time of heat death, or the diameter of the universe, all numbers are basically zero."

[@relzyn5545]

infinity isn't a number smh

[@Dr_Andracca]

@@relzyn5545 Neither is 0 or any negative number in any real sense, but it doesn't stop humans from using their concepts to mentally grasp things though.

[@IceMetalPunk]

@@Dr_Andracca That's... not true. 0 and negative numbers are numbers. Infinity is literally not a number because it doesn't act like numbers.

[@asdfasdfasdf1218]

@@IceMetalPunk *Wrong* , infinity is a number. To be more precise, infinity is an extended real number. It is not a real number, though. Just like i is a complex number, but not a real number. And j and k are quaternions, but not complex numbers. Another related concept is infinitesimals, numbers > 0 but less than 1/n for any natural number n, and their reciprocal, infinite numbers (not to be confused with infinity) greater than n for any natural number n, which exist as hyperreal numbers, though neither infinitesimals nor infinite numbers are real numbers. One way to understand how infinity fits in with the real numbers to make the extended real numbers is through stereographic projection. Each point on the line can correspond to a point on the circle, and infinity would be the point connecting the two ends. Thus infinity naturally completes the circle from negative large numbers to positive large numbers. This is even more important on the complex plane, where it instead sits as the north pole of a sphere. Points of infinity are a central study in complex analysis, where they're called "poles" and determine the value of path integrals based on the topological properties of the path around the poles, such as their winding number. This shows that not only does infinity fit in well with the rest of the complex numbers, but it is a central concept.

[@squish3r]

Fermi guesses are PERFECT for making sure your "precise" calculations make sense. The funniest example I found of it is "How many piano tuners work in Chicago?" The author looked up the population of Chicago, and then guestimated their way to within 5% of the right answer. It was pretty impressive, NGL. Great work, as always!

[@tomcads1604]

The piano tuners one is supposed to be an original one by Fermi myself he used to test students with. I only think it was for New York rather than Chicago

[@mstieler8480]

"The air's moving around at around 2 KpH in here by the way." Two Kyles per Hill? WHERE IS THIS OTHER KYLE?

[@denomaly646]

I actually can't breathe lol

[@TearsOfLa]

he's on the hill of course

[@techstuff9198]

Kilo-pascals per hectare doesn't sound right in any world... But I've seen even worse measurement systems so I'll take it

[@dhayes5143]

He'll be here in another hour

[@YouTubeCommenter8]

What’s even more fun is using the right answer to triangulate, cross reference, and analyze my guesstimation biases

[@Impassive_Bru]

YESSS I was raised badly and adopted this thinking style

[@Impassive_Bru]

Rather, not normal.

[@KickstandOptional]

This is the kind of nerd representation that we need. Good on ya, Hunter.

[@YouTubeCommenter8]

@@KickstandOptional thanks Papa! It’s always been interesting to me to find what trains of thought might have impacted my final conclusions. That way if I ever move past the “guesstimation” phase I know where I probably need more research

[@KickstandOptional]

@@KZbinCommenter8 Using the accuracy of your guesstimates to guesstimate the biases that influenced them. This guy sciences.

[@Ariuss3]

"No this isn't cheating, this is using what we have available." So are you saying that I can just google answers instead of using this method?

[@ShizaanSil]

Not gonna lie, if he estimated the volume of Everest that would be way cooler

[@azuregriffin1116]

@@ShizaanSil I was thinking he'd model Everest as a cone and do that math lol

[@mclason6338]

@@ShizaanSil Did pretty well on my own fermi estimate for this, all in all. Don't recall how high it was. Figured maybe 10 mi, but then recalled I think that's actually Olympus Mons (mars), so dropped it to 2 mi, which seemed more accurate. A mountain is basically just a big triangle if you look at it from the side, but it's not equilateral, so let's figure it's maybe 2x as wide as it is tall. So that's a triangle with a 4mi base with a 2 mi height. Then we consider the 3D rotation, so we make it a cone (circle that moves up to a point) instead of a triangle. I'm thinking recalling that the prefix for volume of cone or sphere is 4/3 (unsure which one), and it's volume, so radius cubed (radius being half the base), and it's a circle, so definitely need a pi in there, then we also need the height, so formula is probably 4/3*pi*r^3*h. This gives us about 67 cubic miles. Converting to feet, we multiply by (5280 ft)^3 = 9.86x10^12 cubic feet. 2.1x10^12 is the actual value. This makes sense as volume constant is actually 1/3 for cones not 4/3 (that's for spheres). That gives us the much closer (within 18%) 2.465x10^12 cubic feet. Showing that it does pay to look up the correct formulas when doing fermi estimates :).

[@1999Fabion]

@@mclason6338 we wouldn't be here if we didn't know what a cone is and what a radius is

[@mclason6338]

@@1999Fabion probably but doesnt hurt to clarify. Also radius in thst case waas half the base of the triangle, so slightly less obvious.

[@dubbynelson]

7:01 "This is going to be difficult, even Fermi"

[@excaliburner9413]

he needs to pin this

[@coolpanda6471]

10/10 comment

[@ReiAyanami8]

"You are technically correct. The best kind of correct."

[@apocalypseinheritor1523]

I feel like this is a Dr Who quote. Cannot confirm.

[@jsimmons3249]

Hermes Estimation

[@taronzgaming7739]

@@apocalypseinheritor1523 Futurama.

[@bregandaerth2529]

To quote the great beurocrat #1

[@inujosha]

The lead burecrat dude in the main Burecrat office from Futurama?

[@TheCharmanderMaster]

I really think this should be taught in more courses than just physics. I was a physics major for 5 minutes before switching to engineering and my physics classes were the only ones to teach Fermi estimations. The thing is, this technique doesn't require any specific vault of knowledge, it just requires that you be taught how to think. Any student could learn this, regardless of major. It also would be super helpful for those annoying job interviews where someone asks you "How many pianos are in New York"?

[@DarkwarriorJ]

I think it should be taught in algebra class. This sort of estimate strongly makes algebra useful and fun; and really is just an application of algebra - relations. Now that I say this, it actually almost seems criminal that it isn't usually taught in ~grade 6 algebra.

[@bulldozer8950]

They actually are taught a bit in high school maths. That’s the exact format many of my teachers have used to convert between units in math class, such as minutes to hours to days, but they never name the Method or acknowledge that it could be used in such a way to estimate

[@DarkwarriorJ]

@@bulldozer8950 Yeah - unit conversion and dimensional analysis are taught; the big leap that isn't taught is the idea that we can really abuse this to estimate things using very rough numbers, get within an order of magnitude, and feel what the order of magnitude means. It's crazy - like, we basically learn all the mathematical skills needed for this by high school; the final leap is realizing how we could use this! I think part of this is that math questions might actually focus too much on highly specific numbers that one may not have on a regular basis. Grading by exactly correct numbers; whereas trying to judge how a student handles a Fermi estimate is more like reading a small essay, I'd figure.

[@Merennulli]

The answer to any job interview that asks "How many pianos are in New York" or similar questions is usually "goodbye". There is a fantasy that those kinds of questions demonstrate problem solving skills, but they really don't. You're correct that Fermi estimation would be the way to address those questions, but Fermi estimation is just one tool that you've either learned or not learned, and it's not a useful tool for most career fields where these kinds of questions get asked. I know your instinct is to think that they must be asking them for jobs where it makes sense to ask them, but they really aren't. And there have been studies done on the efficacy of the questions...and who asks them. The answers to those questions are not indicative of employee performance, meaning it's utterly useless to be asked them. However, being asked them does correlate strongly with bad employers.

[@choty7066]

My guess is 80.000

[@ronrainey1639]

What’s fun about this is once you have tour guesstimation next to the actual number, you can reverse engineer your estimations to find where you were off and posit why you where over/under on a number. Like the dump trucks- the truck might be 2 Kyles tall but the bed starts 1 Kyle up which makes it only 1 Kyle deep overall. Run that calculation and you’d be closer to the actual number. Fun!

[@DialecticRed]

ooh, and I'd imagine if you practiced this enough you'd improve your guestimation abilities as well from knowing how close or far you've been in the past

[@40watt53]

@@DialecticRedgod i love how yall talk about this like its a superpower or something 😭

[@thecrimsonfire4921]

I feel like this should be properly taught in school. Over in Australia I’ve never once heard of this. Just feels like it’s a great way to get people to think about a problem instead of knowing the answer to a problem

[@bishoptrees]

Also, last time I checked, we have great whites down here too... But we don't exist, right flat earthers?

[@alexandergremory9468]

@@bishoptrees Aren't all whites great? Okay, I'm going to go sit in the corner.

[@DialecticRed]

​@@alexandergremory9468White supremacists be like

[@Mernom]

​​@@bishoptreesif you divide by 4 instead of 3, the answer he came up with would be even more accurate...

[@LegendForsaken]

"I've stood next to a large dump truck before" as Kyle halfway smirks at the camera.

[@Princess_kitty14]

Thicc aria now canon

[@vikingbiker]

That killed me.

[@mattscoggins]

That look absolutely cracked me up as well!

[@andrewsparkes8829]

I'm surprised there weren't more dirty "firm" puns throughout this video...

[@dorky2958]

thicc vampire mommy?

[@GarethTheGreat325]

"How many great white sharks are swimming off the coast of california?" All of them, you don't swim on a coast

[@CSpottsGaming]

Badum tss

[@jeramil1271]

"All the live ones." Great white sharks need to swim to breathe.

[@manuelc3671]

Found the A.I.

[@ratdog9]

checkmate rico fermi

[@kamalmanzukie]

off a coast genius

[@Tofu1998]

My freshman Physics teacher told me that you can even estimate how physical equations look like. Start from gathering as much as seemingly relevant input parameters and try to arrange them in an equation in a manner where the units cancel out until they matches the unit of the output.

[@jocloud31]

I sincerely appreciate the segment showing how you did these in real time AND that you got one wrong and went back and fixed it. So often we only see the polished, finished product on KZbin tutorials and it can be intimidating when you try to replicate it yourself. Thank you SO MUCH for showing that process!

[@housecaldwell]

@@AspynDotZip Same here - but ironically the first estimate was closer to the truth.

[@hyliasknight]

the only issue is that the reworked equation was assuming every team in the NBA plays all 100 estimated games that happen in a single season... when only two teams can play in any one game.

[@thepewplace1370]

Yeah this was a blast. Even estimating the size of Mt. Everest by figuring its probably 3 times as wide as it is tall, knowing it's about 30,000 feet tall, and ball parking a dump truck, I wound up about a factor of ten off (99B trucks), factor of 3 for the hair, and factor of 2 for the basketball scores. In the realms those answers wind up being, it's close enough for government work (the difference between 7 billion dump trucks and 100 billion dump trucks seems irrelevant). It's also pretty interesting to see that Kyle tends to underestimate, whereas I tend to overestimate. Useful to know when considering your estimated answers. I've done estimations similarly to this before, but didn't know it was a thing that could yield actually useful answers in so many places. This will be fun to try.

[@spacenerd9499]

Learning and solving problems can get pretty messy

[@bWOOOPdeWooop]

Kyle, you were actually even closer on the NBA question if you're counting the points scored in a normal season. The last two seasons were shortened due to covid so the totals were lower but 2018-2019 there were about 275,000 points scored. I know the point is just getting close by fermistimating but gotta give you the credit you deserve you total sports guy. Love the channel, keep it up

[@GrayBlood1331]

My guess was 230,400. It feels so good to be vindicated.

[@notme907]

but wasn't his calculation way off? why would he multiple 32(Teams) x 100(total games) x 100(points)? This would mean that every Team plays 100 games per season, but Kyle meant to calculate that there are 100 games in total thru all teams per season, didn't he?

[@bWOOOPdeWooop]

@@notme907 no I think it worked out because he was assuming 100 games per season per team

[@notme907]

@@bWOOOPdeWooop ah yeah would make more sense that way.

[@bWOOOPdeWooop]

@@notme907 yeah initially I thought he meant 100 games total when he was thinking out loud

[@Niugnep]

"within a value of 3" " you gotta be impressed by that... unless you're a seal." I may be wrong, but if I was a seal and I knew there are less than imagined i'd be pretty happy.

[@shawnnoyes2776]

and then sad that Gerald was eaten last year anyway :-(

[@mclason6338]

That's still a lot more than you want as a seal.

[@HeWhoComments]

My mind has been corrupted. Every time I hear “dump truck” I can’t help but to think about rear ends lol

[@daniel-zh9nj6yn6y]

Pixar mothers :)

[@harrygenderson6847]

I'd rear-end that dump truck ;)

[@mud4309]

Dude this is so freaky and cool. When Kyle was doing the guesstimations for sharks I did my own even shoddier, even more imprecise measurements going “Yeah that sounds about right”. I guesstimated knowing the distance from my home in Vegas to the coast of California which is 300 or so miles (and I only know due to visiting family on the coast) then went “I think the coast is about two of that distance”, doubled it since I think I recall miles to km being vaguely “double the miles = km” (only just now remembering thats just for metric WEIGHT and I have no clue if that actually applies to distance) then asked from my experience at beaches and very vague knowledge of shark inspired beach hysterics if one shark per kilometer sounded right, then if two sharks per km sounded right - and it did So I ran the Fermi estimate numbers, 1 shark per 2km divided over 600km of coast = about 300 sharks off the coast right now. I sat there waiting to see how insanely off I was because no way my estimate is within a mile of this super smart science man with tons of statistics and figures (vs me, a highschool dropout who, yeah, LOVES hearing about the results of science but struggles to even sorta comprehend the processes and math involved in getting those results 95% of the time) yet LO AND BEHOLD. I WAS MORE SPOT ON THAN HIM This is the only situation in math I have ever heard of where less precise data and figures have been a boon, and I can only assume its due to the fact that he had a lot of precise and neutral numbers, with big and heavier numbers, resulting in a net skew towards larger estimations. Meanwhile my dumbass (probably, I havent checked) way underestimated the distance of the coast and (again, probably) way over estimated the amount of great white sharks that exist on the coast and so those both balanced out to a way more neutral number. I know no one cares or will read this but I just needed to write it down somewhere because this was such a wild and mind blowing experience for me. Never before have I truly experienced and utilized the sheer power and magic that is MATH to this insane degree, all thanks to Kyle. Thank you Kyle this is amazing stuff

[@stevenholt824]

I read it ! Theres every chance you were way off somewhere but it averaged out , more importantly you did it by yourself. I'm into astrophotography and my wife says just Google the pics theyre way better , but that's not the point , it's doing it for yourself. I mean why go camping when you own a house, why watch sport when it's far more fun to do it yourself. Why watch a reality soap when you have your own life to live.

[@wojciechszmyt3360]

At a physics competition in high school that I took part in, there was a special section of problems to solve: estimation challenge. They didn't give any parameter values, we had to estimate them best we could. That was certainly out of my comfort zone, because all the problems would always have precise "here is X and Y, figure out what's Z". It was an interesting experience for sure! Good times :) Not to flex, but I managed to be a laureate on this thing, which gave me an easy entrance to a good university, and I work as a scientist now, and estimation is a very important part of my job!

[@sayanjitb]

Nice to read your experience!

[@saltycreole2673]

I can guesstimate within a few cents all of my grocery bills with admirable regularity. Does that count?

[@flygawnebardoflight]

Yes

[@natanoj16]

Yeps. It does

[@gemma7438]

I think it does

[@fancyf33t295]

Oh yeah. Definitely comes in hand with budgeting.

[@shutupstupid5630]

Yes, yes it does

[@bizichyld]

I am a pharmacist and use dimensional analysis all the time while working, but it applies in so many areas of life. It’s probably the single most useful mathematical tool I’ve ever learned.

[@GabrielHodge]

My man

[@tatesmith4527]

Kill hyle : Advocate for the great ✨TI 89 Titanium✨ calculator Also Kyle Hyle 14:01 : *Procedes to use phone calculator in front of the aforementioned great ✨TI 89 Titanium✨ calculator*

[@aur3ldu05]

"My TI is out of battery". This is the story of my engineering life

[@Virsconte]

Taking a heat transfer final when your calculator is dead. Not fun.

[@aur3ldu05]

@@Virsconte I know that feel... Doing as much as you can by hand and using what's left of the battery to finish it, hopping it doesn't die on you

[@predoarantes4641]

That's how me and my dad solve discussions when we drink

[@GraemeGunn]

What a terrible joke.

[@MarkusAldawn]

@@GraemeGunn I don't think it's meant to be- it's not that unreasonable to grab a napkin and a pen and start writing down numbers

[@davidechols2016]

My dad and I

[@gingercore69]

And the history of guiness world records actually started in a similar way

[@Spolt_main]

@@davidechols2016 shut up dad

[@Magnymbus]

I've been doing a version of this for so long but was never taught it or even knew what it was. Now that I know the process properly I feel more confident in my estimates and now it's even easier. Learning is great.

[@dedlunch]

Same

[@johanbruynsjb]

First time hearing or learning of Fermi calculations. Thank you. And thank you for mention South Africa 🇿🇦

[@BigDaddyWes]

"But this is going to be difficult....... even Fermi."

[@didntask6019]

hehe nice one

[@espinozamarko6118]

"i've stood next to a large dumptruck before" **remembers the vampire's mommy video**

[@randyhelzerman]

This may be the best video on KZbin. Even before you started estimation problems in real time. Which was a really nice touch; indeed totally takes the video to a new transcendent level.

[@thamirivonjaahri6378]

When i was younger, i used to call this intuitive estimation....just imagine dimensions in your head and that's it...no numbers, no calculations, just imagine and extrapolate from the image

[@dubyalast3734]

I’d be interested to see a detailed breakdown of Fermi’s actual estimate from the blast

[@jonathanshaw6784]

At a guess: they would know pretty much their exact distance from the blast (they were the ones designing the experiment and the safety parameters). Inverse square law for distribution of the energy, compare movement to known quantity of TNT explosion, with sanity check from previous estimates. Edit: they would already know the maths for how suspended things move since they used rocket trails to track the shockwave on camera.

[@Arcangel0723]

I think numberphile did a video on this before

[@niagaradrones]

As a Guitarist in front of Whole Foods in Birkenstocks... I feel personally attacked...

[@virtuallycrazy8709]

For a while (idk if it still exists) there was an event in Science Olympiad name Fermi Questions, that was basically just a bunch of random Fermi questions that you get points based on how many orders of magnitude your estimations were off. My favorite is still "How many episodes of anime could you have watched from the birth of the Sun to now?"

[@kathrinsides2838]

I really enjoyed watching you think through the problems that you were working on. I’m a former teacher, and I really enjoy your channel. You are a great teacher, and I’m going to recommend you to a couple of my friends who have kids who are in school. I think that they would get a lot out of watching & learning from you. Thank you for what you do.

[@maxwilson7001]

Thank you for teaching

[@cornofthechildren]

I use this process everyday just for fun, I didn't even realize it had a name.

[@heroiuraresjustinian4681]

Lol same

[@trybunt]

Yeah, I've actually calculated the number of seconds in a year before... And how many meters per second I drive, how long it would take to walk around the world, how many generations there has been since life began.... so it was funny to see the weird stuff I subconsciously do in my head being explained as something useful

[@narx4cancer]

same

[@bulldozer8950]

@@trybunt remember. It’s wasting time, unless you write it down. Then it becomes science.

[@3nertia]

Me as well

[@progressweapon6180]

So, because of this video, I just learned that this is how my dad taught me how to do math WAY back in elementary school... Which explains not only why I always loved math, but also why my math teachers hated me

[@techstuff9198]

@@AspynDotZip That is up until we start throwing people into the interstellar expanse and The Intergalactic Void.

[@CSpottsGaming]

I didn't know this but I've been using Fermi estimates for years! It's such a convenient way to get a ballpark number. Yeah, you're never going to be close enough to get a homework problem correct but it makes for a great method to estimate weird things that come up at the bar between friends.

[@TheFinagle]

"I have stood next to a big dump truck before" describes one of the mini trucks you see in cities not a normal one thats 2 or 3 stories tall and 3 lanes wide

[@Chris_Cross]

And yet he was still way under.

[@GeekPsychologist]

So apparently I've been using Fermi estimates all my life without knowing they had a name. Neat, I think.

[@Parodox306]

It is neat that you think

[@queenannsrevenge100]

@@Parodox306 - I wonder if the method was used before Fermi, whether he actually created the process or just popularized it. I’d like to believe someone like Archimedes or one of the Arab mathematicians came up with it, but sometimes the simplest solutions really do take a long time before someone envisions them.

[@Parodox306]

@@queenannsrevenge100 I feel like the technique is something many people were aware of well before Fermi (look through the comments and notice how many people used it before knowing it had a name; hell, I've personally used it plenty of times before know who Fermi was), but he codified it in a way that made it more accessible. It's likely that many of the greats throughout history had similar strategies but used different language to describe the process, or just took it for granted, thinking it's what people naturally do.

[@christianstarr9188]

@@Parodox306 I would put my money on your last guess. When I was in middle school our science teacher covered dimensional analysis for simple unit conversions, because it's a simple format, and I had the same "aha" moment the comment section is having now.

[@bipolarminddroppings]

I have been working stuff out like this my entire life, no one ever taught me it, it just seemed a logical way to guess things. Never knew it had a name and a defined method. You learn something new every day.

[@chairpara]

Am I the only one that did this in like forever without even knowing that there is a specific term for it?!

[@chairpara]

And the best part is that today, in school, I asked a colleague to ask me a question that could be estimated and then checked on google. She asked me how many mosquitos are there. I said that each human has about one mosquito bite per night and that mosquitos only live in the summer and half of spring => 1/3 of the year so 100 days. This would mean that there are 100 mosquitos per human. But I remembered from an insect lesson a few years ago that a mosquito feeds on about 5 people so I got that there are 20 mosquitos for each human. And because there are 7.5 billion humans => there are 150 billion mosquitos. Do you want to know the actual number of mosquitos? 178 billion! Only 28 billion off!!! That’s pretty cool...!

[@nachiketh3650]

Exactly my thoughts. Always felt this must be normal.

[@orangus01]

@@chairpara How do you know that the answer you found googling, wasn't itself fermi estimated?

[@chairpara]

@@orangus01 🤯 that’s some out of the box thinking right there

[@RealMaltigow]

No you are not. 😅

[@codemaster2861]

My high school physics teacher thought me to do this I was the only one in my college that knew about this so I'm glad it's being shared by someone so influential and well known

[@Closer2Zero]

I don’t know about anyone else, but my favorite part of each episode is the section after he says he doesn’t know what or how he’s going to fill the time as the Patreon names go by. It’s a very wonderful wrapup or behind-the-scenes moment for each episode that I really appreciate and look forward to

[@JimRFF]

Video title "How to Guesstimate Like a Genius" Uploaded: 1 minute ago Me: I'm already 4 parallel universes ahead of you

[@LuxGamer16]

Video title changed. I see this alot actually. Confuses me on why tho

[@archangel8444]

I've done this my whole life, but now I have a better understanding of something I did automatically. Thank you, I love all your videos man.

[@nicholasstapleton6108]

Hey! Fellow educator/nerd here- I appreciate the real time problem solving / computing section of the video. It really helps build a human connection between the viewer and the host. Keep up the great work, Kyle & team! :)

[@JoshuaWeirdo]

Kyle: "I've stood next to a large dump truck before." So you're saying that Aria is thicc?

[@derpinator4912]

You saw the way he looked up after he said that. He knew what he was saying.

[@3dpprofessor]

Have you seen her Twitter? She ain't just a pretty voice. Actually, she could twist your head right off.

[@jasonwillows5239]

Kyle: Asks for Casio TI-84 sponsorship Also Kyle: Has to use phone because his calculator is out of battery

[@reichstein011]

If TI would just sponsor him then maybe he could afford some fresh batteries :)

[@reignman30]

Sounds like he should have asked for a battery sponsorship.

[@devaraiuzuchiha1982]

When you showed the result of the shark estimate I wondered how you came to this conclusion, but then I actually got to 972 using only the given numbers and I have to say I`m kinda proud of myself. As always thanks for the video and keep going my favourite science communicator.

[@brandonejem8620]

I've done quite a few calculations like these my whole life. It's fun to guestimate answers like these. What I didn't know was that it's okay to be off by a factor of 2 or 3. I always felt like this was way too much to be considered close.

[@Buphido]

At least in science that deals with big numbers, anything that lands in the same number of digits, or same order of magnitude, is extremely close. Even being off by a factor of 100 (two orders of magnitude) can be considered fairly close in some contexts.

[@Cipher_Paul]

That just reminds me about the scientific method of Descartes which could theoretical solve any problem and Fermi is the dude who seem to have perfectly understood this mindset.

[@EisenKreutzer]

I mean, Descartes solution to everything was that an evil genius was trying to trick him. So I guess that is theoretically an answer to any question.

[@oompalumpus699]

Me after watching this video: "You know, I'm something of a mathematician myself."

[@DoomRater]

What's really cool about this is I've been seeing my favorite geologist using these tricks on Quora to great effect. And the more relevant figures you can think up and get hard numbers on, the more accurate the calculation at the end. The best part is how so much of it is just arithmetic. Elementary! Best part is, you do it enough and you can use emotion to feel a problem out since the data will be within reach of your working head.

[@Zillano]

I love the whole process of the equation, it literally shows one, everyone makes mistakes and two, goddamn is it hard but possible. Just takes a lot of good understanding of what it is your working with.

[@danielevans5160]

I recently had to do a Fermi Estimate for my work dealing with an issue on an automated process. The short explanation is that we had two bits inside a PLC (Programmable Logic Controller) turning on at the same time that cancel each other out. It went something like this: We make around 400 units per day, we run this process once per unit, this process has about a 1 second window to fail, the PLC refreshes at a rate of around 50Hz (50 times per second), and the chance of the two bits turning on at the same time would be close to 1/2,500. Doing the math gives an answer of 8 times per day, and that was only off by +/- 2 depending on how bad the day was.

[@yoshitheonly]

17:07 He knows our thoughts and he preemptively disapproves 😂

[@BigDaddyWes]

(Insert joke about Lady D's butt)

[@Dinoguy1000]

Instead of googling it, you could do a Fermi estimation of the volume of Mount Everest by approximating it as a cone with a base length and height of 29,000 ft, which gets you a volume (via v = pi*h*b^2 / 3) of ~6.4 * 10^12 ft^3. Combining with Kyle's estimate for the volume of a dump truck, this gets a Fermi estimation of ~5 * 10^9, or 5 billion dump trucks, considerably closer to the value of 6.4 billion dump trucks listed at the end.

[@skater15153]

Literally how I've done math stuffs in my head forever. Now I have a name for that haha awesome video as usual

[@MrBlack0950]

This is basically the "lemme math it out" equivalent of pulling things out of nowhere. I can get behind that.

[@WarlandWriter]

Thanks for this episode. I loved it when you first demonstrated this on that livestream on a channel that shall not be named but was never able to find back what it was called. This is such a great tool, you're doing the basilisk's work with content like this.

[@siukong]

In principle I like the idea as it's an analytical way to make estimates. And just as a good thought experiment to keep your mind sharp. However, I think the importance of being confident in your assumptions was very understated. It's all well and good to try to break down the problem into a series of smaller guesses and hope that the over- and underestimates will generally cancel each other out. But all it will take is for just one of those broken down guesses to be WAY off to scuttle the whole process. This is why I suspect Kyle immediately knew he shouldn't estimate the volume of Mount Everest: a mountain is just so unfathomably huge and irregularly shaped that it would be extremely difficult to do back-of-the-envelope math and be somewhat accurate with it. The chances of being extremely off the mark are just too high. This to me is one of the big pitfalls of this method, and why I can't envision a whole lot of scenarios where the tradeoff of accuracy for speed would be worth it. Short of corner-cases like being camping in the wilderness somewhere, or having an extremely time-sensitive issue where the clock is ticking and speed is imperative. I'd rather someone just look up a few more of the figures to have a better grounded sense of the problem. I'm also uneasy with the idea that for many of these problems - unless you're able to find an extremely relevant data source (like an actual measurement of some strange elderly Luddite's hair, or a direct sample of shark populations off the coast of California) - your "official" answer that you consult to check things is itself no more than a slightly refined case of a Fermi estimate with a more accurate foundation of broken down numbers used to calculate it. I think the "sanity check" step is another one that was not emphasized enough. People need to really think of what they might have missed and how they might be wrong. There are many of these problems where I could see there being mitigating factors that would make the real result strongly diverge from your estimate. For example, for the hair problem it doesn't account for the fact that hair grows at different speeds throughout our lives (hair growth slows as you age). Also, there's something call "terminal length" which is the length your hair stops growing at (somewhat of a misnomer as it doesn't actually stop but reaches a sort of equilibrium where hair loss and other wear and tear from damage happens fast enough that growth can't keep up with it). In the dump truck example, moving even a moderately massive amount of material, we'd have to also account for spillage, settling, and erosion from the wind/elements, among other things. Even at the scale of a major construction site I'm sure these are important factors, let alone for a hypothetical scenario involving moving an entire mountain.

[@McAwesome1988]

I knew there had to be a name for it!!! I've been able to do pretty "accurate guesstimates" since I learned averages and fractions, it clicked for me. I'm really happy to hear it's a thing and that I'm not just randomly pulling numbers out of my butt. I knew I subscribed to you for a reason!

[@matthewlantz1677]

I remember learning about this in high school. We were asked how many piano tuners there are in Chicago.

[@r3ttgaming177]

13:45 Well...... There goes that sponsorship. I'm about 90% sure of that, going by the Fermi estimate.

[@dafire9634]

About 4mins late for the correct estimate

[@bwalters7777777]

I already do this a lot - all just in my head - and then quickly forget about it. I didn't know there was such a thing as a Fermi estimate. Now I should keep track of them and actually see how accurate they are!

[@Aviator27J]

I feel like this is how we all think when estimating things of this nature, only we don't necessarily think about the process. I suppose we do sometimes, if we're explaining it or trying to work it out on paper, but mostly it isn't a mind blowing thing. I mean, cool video though--don't get me wrong!

[@Idontknow-vm1iy]

You’d be surprised, a lot of people don’t estimate, they guess.

[@Ray-uf8dj]

I absolutely adore this new method of thinking, however I really wish I could see the equation Fermi used to estimate the blast’s equivalent of TNT.

[@lancebradshaw4829]

If you know how much fissile material was used, the calculation is fairly straightforward.

[@Ray-uf8dj]

@@lancebradshaw4829 Do you know how much was used? If you don't, I'd love to see the calculation of how to work it out, even just as a partial equation. I don't know much about the topic but I'm really curious.

[@lancebradshaw4829]

@@Ray-uf8dj Some quick research says that the core weighed 6.19 kilograms (13.6 pounds). However, it was a plutonium-gallium alloy, so I don't know how much of that was actually plutonium. Working out the maximum possible yield of a given mass of plutonium would involve looking at the difference in mass between the initial plutonium and that of the elements that are produced by the reaction (the so-called "mass defect"). The products weigh less because a small amount of the mass is converted into energy. I'll probably try to send an example calculation on your profile or something later.

[@thomasboyd1402]

Huh.. Forgot that Kyle escaped the formless void.. I'm happy for him.. I fear for the world, though.

[@andykeskimaki5409]

I got through undergrad as an electrical engineering major with a Ti36 Pro. It has every constant I ever needed preprogrammed on it. The only times I ever broke out the titanium was to double check a graph. IMO, for the average person a 36 Pro is all they'll ever need P.S. Love the content and keep up the great work my dude!

[@fucksusanwojcicki]

i feel so validated in that i have been using basically this exact method to calculate various things as far back as i can remember

[@darthflash6994]

You're one of my science heroes Kyle.

[@givenjoy]

I guestimate this will be a great vid!

[@tatuvarvemaa5314]

Guestimations usually arent this pin point...

[@givenjoy]

I would make Fermi proud ..

[@nickiaccarino2481]

On the basketball one, you needed to divide by 2. There maybe be 32 teams (or however many) but since each game has two teams, by counting how many points were made per team per game for all teams, I think you double counted teams. Since one game has two teams, and you calculates points per game per teams times # of teams total, when it should’ve been times # of teams divided by 2. This would mean your answer would be closer to 160000 points. Which is much closer to the “actual” amount.

[@zeanyt2372]

I've been using Fermi estimates to calculate the FPS of modified dart blasters and horsepower figures for years now. I've also modified the system to use the real world examples get smaller margins of error for each factor, the results have been surprising. I can normally guess within 10 FPS of the final muzzle velocity of any modified blaster, and about 100 horsepower of any vehicle. Apostle been using us to make hypothesis about quantum physics, which for a Sci-Fi fan is a lot of fun.

[@sergioortiz8219]

I read a while back that some big tech company would ask its job interviewees how many piano tuners there are in Chicago to see how they would go about solving it, presumably expecting them to use some variation of unit analysis.

[@miranor6941]

"Thats definitely worthy baby~" I laughed so hard hahaha

[@apocalypseinheritor1523]

Hey, I think he is Smart Space Dandy.

[@Lobod287]

This is an awesome tool That I'm sure to start using more of. Ive made similar estimates before but this feels much more refined. I even got within 20 inches on that hair growth estimate

[@Lericah4902]

I love how this is so intuitive I had no idea I was doing it. I use conservative Fermi estimation in all my budgets. ~2.5 * ~10 ~= 25. Call it 24 to be safe; And then whatever values your budget spits out are close enough but will trend downward in your favor; So I could accidentally splurge on that plushie,tangent; I love semi-colons, I had to get from Kyle but I know that I have about $500 of spare money between my Budgeted limit and my Actual limit so that extra $20 doesn't matter and I can instead focus on why my connection string closes before I can complete my write operation.

[@georgprime4665]

I just noticed Kyle's mustache parts like an insects mandible when he's really emphasizing words and I can't unsee it....

[@apocalypseinheritor1523]

I'd curse you for this, but I find this to be an interesting thing to know.

[@sirapple589]

He’s a tarantula.

[@Agg1E91]

Damnit! Now *I* can't unsee it, either! I need to stop reading comments...

[@tatuvarvemaa5314]

Fermi estamation sounds like the most badass real life super power. Or the most smart ass thing in the world.

[@TimidTortoise1988]

I’ve never heard of this before. Incredibly cool. I’m going to try and think of some things to use this on.

[@boas_]

For the shark question, I did this: Lets say the shore area is 25km from the coastline Lets say that the coast is a 500km long, just order of magnitude Lets say that each shark has a territory of 5x5 km So the amount of sharks = 25×500÷(5×5)=12500÷25=500

[@Paraselene_Tao]

Haha, for the great white shark I simply said, the coast of California is about 840 miles and there's maybe 1 great white shark per mile of coastline. I got 840 great whites with only 2 guesses.

[@chrisdudethe1]

When I was a kid, my school did a "how many jelly beans are in this bottle" challenge. I used this breakdown to accurately guess the winning number within 10 beans. I felt super smart for a faith grader.

[@dankone3]

Aw, so what happened to you

[@7opher619]

Faith grader eh? Soo, a Christian school I assume.

[@Ismael900G]

I did the hair one myself, starting at how much my hair had grown in a year and a half, and I ended up with 17m for a lifetime, quite close to your answer, so probably our base estimations were somewhat right (I used 0.6mm per day and up to 80 years of life). I'm guessing (without looking it up) that hair's growth ratio decreases at some point. Also, excuse my english, not my native language.

[@Buphido]

I didn’t cut my hair for like 1.5 years in which it grew like 25cm and I estimated the human lifespan to be like 75 years, so 25cm * (75/1.5=50) = 12.5m. My personal experience gave me a pretty good estimate for long term hair growth I guess.

[@maxwilson7001]

Your English is perfect

[@skylark7921]

You’re actually right! There’s a mechanism in your hair follicles which basically decides how long your hair follicles will produce hair before ending the strand (thus causing it to fall out) and starting a new one. (That’s why your leg hairs don’t usually grow as long as your head hairs, but a human with higher testosterone like most men will get longer hair on their face which can match their scalp hair) This can be very different depending on genetics, diet, and circumstance. Stress triggers your follicles to stop growing hair, and a low protein diet means the follicles can’t get the required materials to make the hair. But yeah, if your follicles never stopped producing hair you’d probably reach about 17-18 meters, but in reality the growth on average stops at about 10 meters

[@Ismael900G]

@@skylark7921 I found out about the stress thing the hard way, hoping it's kinda reversible or something, though I can't get rid of the stress...

[@unclecreepy4185]

The example of canceling out units is what I would have students to to figure out crazy things. Like, “say a tree grows 5 feet in a year. How many miles per hour does it grow?”

[@MahmoudElgassier]

I had no idea this was called Fermi Estimation. I just kinda roll my eyes backwards into my sockets (that's not weird, you're weird) and plug some figures to estimate values like jelly beans in a jar. This was fun.

[@mdinkel]

I've heard AvE refer to a similar process as dead reckoning and it's a surprisingly usefully tool

[@vincentochs637]

AvE is an amazing creator and very smart and secretive.... Almost like a supervillain

[@skrounst]

I never knew that this method had a name, I used to use this to DESTROY my friends in trivia crack. Just take some sort of statistic that I DO know out of the question, and kind of work backwards from there to get close to the answer. GG Fermi, you made an intuitive, logical estimation formula. Also GG Kyle, you made a BANGER of a video!

[@khloeg1649]

i have a TI 36x pro, will that do?? and honestly, this is a pretty fun video to follow along with. I haven't used dimensional analysis since my chemistry class a couple years back, but it's surprisingly easy to get back into doing, and it's surprising how close you got those estimates based on very little prior knowledge