One Weird Math Trick Estimates ANYTHING (Fermi problems)
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- Опубліковано 28 вер 2024
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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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Police officer: Sir, do you know how fast you were going?
Me: *Inhales*...
I don't know for sure, but my guess is about one half a moon distance per shark attack
But officer, speed is relative!
I'm reasonably sure I didn't break the sound barrier.
@@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.
This made me laugh so hard I almost peed my pants
I remember doing these kinds of exercises in school. My dad calls these SWAGs: Scientific Wild A$$ Guesses
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! 😊
Show your SWAG! 🤣
@@MaryAnnNytowl you're welcome! 😀
I doubt any dad to be that cool
That's actually a proper phrase! Wikipedia it lol
Thanks Kyle, now I can get every question on my math tests almost right.
"I have approximate knowledge of many things"
@@maoman4855 would this count as a shitty superpower?
@@zzz_zzz_ZZZ_zzz_ZZZ_ZZZ_Z_z-ZZ yoooo definitely should be
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
@@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
Title: How to estimate anything
Me: All non-infinity numbers round to zero
"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."
infinity isn't a number smh
@@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.
@@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.
@@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.
"The air's moving around at around 2 KpH in here by the way." Two Kyles per Hill? WHERE IS THIS OTHER KYLE?
I actually can't breathe lol
he's on the hill of course
Kilo-pascals per hectare doesn't sound right in any world...
But I've seen even worse measurement systems so I'll take it
He'll be here in another hour
"what's 9+10?"
Enrico Fermi: "21"
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.
*29
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.
@@Joseph125 engineers, amirite?
@@Joseph125 π = √g = e = 3
"You are technically correct. The best kind of correct."
I feel like this is a Dr Who quote. Cannot confirm.
Hermes Estimation
@@apocalypseinheritor1523 Futurama.
To quote the great beurocrat #1
The lead burecrat dude in the main Burecrat office from Futurama?
I love how the Drake equation is simply a Fermi estimate, jumbo sized.
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 ^^
@@mlembrant I do it too for all prep
Also yes it basically is.
Yeah same, whatever that means
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…
"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?
Not gonna lie, if he estimated the volume of Everest that would be way cooler
@@ShizaanSil I was thinking he'd model Everest as a cone and do that math lol
@@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 :).
@@mclason we wouldn't be here if we didn't know what a cone is and what a radius is
@@1999Fabion probably but doesnt hurt to clarify. Also radius in thst case waas half the base of the triangle, so slightly less obvious.
"Is that a firm estimate?"
"No, it's a Fermi estimate."
"Isn't that what I just asked?"
"almost"
@@dinamosflams *well yes but actually no*
@@dinamosflams lmfao
Three replies in and I already love this thread
@@anchovybushwack472 make that four.
"A few years ago when I was trapped in a formless, emotionless void-".
Ah, so working on Because Science
Yes, that's the point
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
I have ascended, I've received the fabled AxxL reply
@@niamhythedegen *AxxL
@@AxxLAfriku ah yes of course, how foolish of me
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"?
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.
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
@@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.
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.
My guess is 80.000
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
Also, last time I checked, we have great whites down here too...
But we don't exist, right flat earthers?
@@bishoptrees Aren't all whites great? Okay, I'm going to go sit in the corner.
@@alexandergremory9468White supremacists be like
@@bishoptreesif you divide by 4 instead of 3, the answer he came up with would be even more accurate...
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
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.
What’s even more fun is using the right answer to triangulate, cross reference, and analyze my guesstimation biases
YESSS
I was raised badly and adopted this thinking style
Rather, not normal.
This is the kind of nerd representation that we need. Good on ya, Hunter.
@@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
@@UA-camCommenter8
Using the accuracy of your guesstimates to guesstimate the biases that influenced them.
This guy sciences.
"I've stood next to a large dump truck before" as Kyle halfway smirks at the camera.
Thicc aria now canon
That killed me.
That look absolutely cracked me up as well!
I'm surprised there weren't more dirty "firm" puns throughout this video...
thicc vampire mommy?
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.
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 UA-cam tutorials and it can be intimidating when you try to replicate it yourself.
Thank you SO MUCH for showing that process!
@@AspynDotZip Same here - but ironically the first estimate was closer to the truth.
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.
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.
Learning and solving problems can get pretty messy
I can guesstimate within a few cents all of my grocery bills with admirable regularity. Does that count?
Yes
Yeps. It does
I think it does
Oh yeah. Definitely comes in hand with budgeting.
Yes, yes it does
I’d be interested to see a detailed breakdown of Fermi’s actual estimate from the blast
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.
I think numberphile did a video on this before
"i've stood next to a large dumptruck before" **remembers the vampire's mommy video**
I use this process everyday just for fun, I didn't even realize it had a name.
Lol same
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
same
@@trybunt remember. It’s wasting time, unless you write it down. Then it becomes science.
Me as well
7:01 "This is going to be difficult, even Fermi"
he needs to pin this
10/10 comment
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
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?"
Kyle: Asks for Casio TI-84 sponsorship
Also Kyle: Has to use phone because his calculator is out of battery
If TI would just sponsor him then maybe he could afford some fresh batteries :)
Sounds like he should have asked for a battery sponsorship.
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
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.
Same
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.
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.
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.
First time hearing or learning of Fermi calculations. Thank you.
And thank you for mention South Africa 🇿🇦
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.
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.
Thank you for teaching
Am I the only one that did this in like forever without even knowing that there is a specific term for it?!
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...!
Exactly my thoughts. Always felt this must be normal.
@@chairpara How do you know that the answer you found googling, wasn't itself fermi estimated?
@@orangus01 🤯 that’s some out of the box thinking right there
No you are not. 😅
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.
If you know how much fissile material was used, the calculation is fairly straightforward.
@@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.
@@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.
13:45 Well...... There goes that sponsorship. I'm about 90% sure of that, going by the Fermi estimate.
About 4mins late for the correct estimate
This may be the best video on UA-cam. 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.
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!
Huh.. Forgot that Kyle escaped the formless void.. I'm happy for him.. I fear for the world, though.
I just noticed Kyle's mustache parts like an insects mandible when he's really emphasizing words and I can't unsee it....
I'd curse you for this, but I find this to be an interesting thing to know.
He’s a tarantula.
Damnit! Now *I* can't unsee it, either! I need to stop reading comments...
"All the units add up, multiple across the top, divide across the bottom and then BAMM!!, you just added some of that sweet sweet Spice Weasel"
The problem with the Drake Equation is that several of the variables are absolute unknowns (e.g. the probability of life developing on a planet). They can be anywhere from 100% to 1 out of the total number of planets in the universe (that 1 being Earth). So it's categorically a useless equation.
In the extraordinarily unlikely situation that we discover life elsewhere in the universe, that would change everything and make the equation useful as we'd then have a second instance.
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.
Fermi estamation sounds like the most badass real life super power. Or the most smart ass thing in the world.
These estimation problems are usually interview questions. The recruiter is more interested in how you estimate stuff instead of how close you were to the answer. "How many pizzas are baked in this city per year?" and "How many tampons are discarded every year in the country?" are some that I remember off the top of my head
Kyle: it's difficult to know off the top of your head how many seconds are in a year.
Math/theater overlap kids: let me tell you how to measure a year
I've heard AvE refer to a similar process as dead reckoning and it's a surprisingly usefully tool
AvE is an amazing creator and very smart and secretive.... Almost like a supervillain
I had a professor in orbital mechanics who could guesstimate distances, figures, orbital times, etc. this way *without a calculator* and be within 10%-20% of the real answer. It was very impressive.
Bravo for being 100% honest with those calculations.
This is really cool! I used the Fermi estimate and got these results:
1. 8cm/month x 12month/year x 85years/lifetime = 8160cm = 81m per lifetime. This is off by quite a lot (factor of 8)
2. I didn't even try to guess this one because I know nothing about basketball, I don't even know how many games are played each day, how many days does the competition last, and how many points the players score in one game
3. I know Everest is around 8km tall, and I've seen pictures of it so I assume it has the shape of the cone, the base is about 20km in diameter because it looks right. Then I estimate a dump truck is 5m x 3m x 3m in volume, so doing the calculations [(1/3)*8π*10^2*10^9] / (5*3*3) = 1.86*10^9 dumptrucks which is 1.86 billion dumptrucks. I'm surprised how close I got this one
Me: That seems too big for a dump truck
Me, later: mhmm
I was thinking the same. I think he was estimating the full size of the vehicle vs the the carrying space.
Ah yes, the infamous Nuffield A levels Physics Estimates question, circa 1982. The most single useful lesson of the entire course, for me anyway (who didn't become a physicist), because it works for absolutely any business situation where you are trying a first guess at "is this worth doing, and if it is, do I have the resources?".
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.
My chem teacher taught me this, and it great. You can use it for anything.
0:15 what she sees
My physics teacher for three years came up thru the school system before everyone had calculators. He could solve problems involving the math side of it extremely accurately. He could do the basic arithmetic in his head and he had things memorized like the squares of numbers up to 20 squared, square roots of small numbers to three decimal places, sin, cos, and tan of the most important numbers to three decimal places, log base ten of important numbers. Plus he used various arithmetic tricks to make it easier and faster. Imagine the time saved when doing a physics exam when you don't have a calculator.
Today I learned what the technical term of how my brain has worked my whole life, genuinely what a trip. To think a famous scientist created a whole mathematical principle with which my brain would work decades later is just mind blowing.
Holy crap, I think that was my question about your hair to the moon!! 😱😎👍
I think one of the issues with the accuracy of your guesses in the last section may be from the number of properties you used to calculate them. It seems to me the more properties you factor in, the more likely high and low estimates are to cancel each other out. If you start from a single area of confidence, and then have only one other property (which is a complete shot in the dark), then that will just throw off the confident number, making the final number as far off the mark as the less accurate property is.
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.
Once when I was a math tutor, my 9th grade student didn't understand why he had to learn scientific notation. So I told him to sign his name as small as he could make it and, while he was doing the next problem, I was going to calculate the number of signatures it would take him to circle the Earth.
Signature was about 2 cm in length, the circumference of Earth is 45,000 km. 4.5x10^8 divided by 2x10^-2 and boom. 9x10^10 signatures.
When I was done before he was done with his problem, he realized the power of dimensional analysis and scientific notation
I've done that my whole life, no one ever taught me, I just assumed thinking this way was normal for everyone. Fascinating to find out there is scientific rigor behind it! 🤔
Fermi Equations are really great for worldbuilding. You can get really close estimates based on some kind of rules that you've set for yourself, and create a realistic enough world for yourself!
These are basically Order of Magnitude Estimates and the general process has probably been around since we discovered mathematics. In Canada they start this in Math 4 or 5. Fermi and countless other scientists use it daily without thinking. He used it often, publically. He’s one of the most famous scientists in history. So…bang.
17:08 mans knew what he was saying
I’ve been doing this for years, thinking it was normal estimation. I only did two of the problems. I guessed 140’ for hair using about a foot every six months times about seventy years. (I guessed eighty years for life, but subtracted about ten for childhood.) then I estimated 2.6 trillion’^3 for the mass of Everest by fudging a few numbers, multiplying 27*7*13.5ish*1,000,000,000. Then I calculated a dump truck as 15*10*10, and came up with around 1.7 billion.
This technique has actually helped me understand and practice math a lot over the years.
At 16:17 and 20:10, it's a trick question. Provided it could be fueled and operational long enough, given the necessary labor, it would take one dump truck to haul away all of Mount Everest. What you estimated was how many trips that dump truck would have to make.
I had a program that calculated Laplace and inverse Laplace on my ti89 (in 2000) Shout-out to whoever developed it back in the day, you helped me through college.
I got 100 in the shark estimate and that felt pretty good. I was a little sad that my approach was so different though because I realized it was easier to estimate "miles per shark" than "sharks per mile." I really wanted to hear Kyle say "miles per shark."
5:12 - "...No human's hair, laid end to end, would never reach the moon."
Double negative is proof positive - all of us will, one day, have enough hair to the moon. Kyle says so. Cheers Kyle!
Y'know, the distance to the moon, is funnily enough something I know off the top of my head.
My dad keeps asking his devices that question, whenever he wants to check if they're working XD
Fun fact: I use metric system and estimated 45 cubic meter for the dump trucks. 2m high, 4m large and 6 meter long + an extra 5 cubic meter of material from the lump. this is so close from your 6ft, 12ft and 18ft dump truck.
I just assumed that this was how all people estimate things. Isn't it?
No. It definitely is not.
my high school senior year honors physics teacher drilled us with dimensional analysis problems... best 'magic trick' i ever learned
I used to have an 89 Titanium from 6th grade through AP Calc in 12th grade (the reason I passed, and only got a C [calculator/no calculator portions]) But for college I upgraded to TI's Nspire CX CAS when the batteries eventually leaked after the 89's long tour of duty. Still what I use to date when I need something more than a phone calculator, but doesn't warrant firing up MatLab. Hopefully the Li-ion battery never leaks!
Step up your product placement Kyle if you want that brand deal! (having a jest here)
I use this all the time when people don't want to give time estimates -
"how long will the task take?"
"I don't know"
"you must know the ballpark figure?"
"No"
"1 hour or 1 week?"
"2-3 days"
Good enough for me 🤷♂️
Hilarious note, for the dump trucks I also got 1.6 billion trucks...
20 cubic yards in a dump truck, which 9 cubic feet to a cubic yard gives 180 cubic feet per dump truck.
I guess everest is I think less than 2 miles high, and given a cube in volume in a cube it was probably only 1/3 of the volume of a cube since it's roughly a wide pyramid, I estimated a volume of 2 cubic miles.
5280^3*2 / 20*9 = 1.635532800 billion dump trucks
I get this in principle, but I think we have different definitions of "close."
getting to the same order of magnitude while using only numbers you pulled out of your ass from values you kinda remember is impressive.
Depends on what's being estimated and the orders of magnitude involved. It's hard to imagine a context in which the shark estimate would ever be relevant, but what if you came to the same numbers regarding money in your checking account? Guessing you have $900 when you have $300 - $400 can cause some major problems if you go to pay your $800 rent without moving money around.
Really useful to estimate between celcius and ferenheight. Just remember, 0c is freezing, 100c is boiling, and 21c is comfortable
9:49-10:00 I like to think he said "shut up" to some random employee walking down the hall
Damn Kyle, that worked really well. I remembered Everest was about 29000 feet tall and cement trucks hold about 10 cubic yards of concrete. I calculated the volume of everest by pretending it was a pyramid and using that formula and guessed the size of the base by holding my fingers in a roughly Everest shape to guess the size of the base as half the height. V= 2.32 x 10^12 cubic feet. Then, since dump trucks are bigger than concrete trucks I just changed the units from yards to meters and ran the calculation. V= 10 cubic meters. Converting Everests volume from yards to meters and divide by ten. Number of dump trucks: 6,569,508,409.3
Remember: 1 day = 1440 minutes.
It's about 1/7th of the week, so 10k = 10000 minutes per week (underestimate).
About 520k minutes per year, which times 60 gives about 31.2 million seconds.
It's underestimate, plus extra day we missed (14*52 = 364), so let's round it up to 31.5M.
Quite a good guesstimate, I suppose ? ;-)
Or even FASTER!!
Very good method for "fast guessimation" is to group some numbers or make them into some fractions, like:
365 days ~ 1/3 of 1000 days
24 hours ~ 1/4 of 100 hours
That gives us 100k / 12,
times 60 gives us 500k, (60/12=5)
times 60 again gives us 30 millions.
Close enough, I guess :)
If you want to move Everest, Use the Caterpillar 797F Dump truck. It can haul 330yd^3 so long as that volume doesn't exceeded a net weight of 400 US Tons.
It is the highest capacity dump truck on the market (at time of posting) it does have a bit of a fuel consumption issue though, I think it burns an estimated 15 US gallons of diesel per mile.
After watching this I'm getting the impression that you should divide by 2 once you get your answer.
I've been doing this on a smaller scale all my life and never realized there was an actual name for it.
A Fermi estimation of the relativistic kind would be fun.
If you had estimated between your first and last guess, you would have landed on the points per basketball season almost exactly, thus to me you got that one beyond accurate.
I use this all the time and just like you said on most things you can get well within one order of magnitute with numbers, you can do in your head.
This is also why this is such and good tool to either estimate if something is possible or imposible.
If a claim says something is well outside one order of magniture of you guesstimation it is likely not correct.
Ever wanted to be that one character in every sci-fi show? Well now you can! Never tell me the Fermi estimate!
I was playing along with a couple of those questions and I did the dump truck question totally differently. First, I guessed the height of mount Everest was 25 thousand feet (apparently it's 29,032). Then, I guessed the height of a dump truck was 20 feet, so it takes 1.25 thousand dump trucks to match the height of Everest. Then, round Everest and a dump truck to perfect cubes, and guess that a dump truck can hull an amount equal to its volume, then it takes 1,250^3 = 1,953,125,000 (or 2 billion-ish) dump trucks to hull all of Everest. If I knew Everest was closer to 30 thousand than 25, then I would have gotten 3.3 billion.
For the basket ball, I didn't know how many games there are in a season either, so I guessed that there are 32 teams, guessed that they play once a week, and guessed that a season is half a year (26 weeks), thus 26*16 = 416 games in a season. So 200 points per game gives 83,200 total points.
very cool.
I think it would probably be prudent to apply a final factor after you arrive at your "original" answer every time - an "overall confidence/adjustment factor". Not anything that would change the order of magnitude of your answer but could change it by as much as a factor of 2-3.
I think a lot of us probably would've guessed the hair answer was on the high side and the everest answer was on the low side. So if you look at your "original" answer and take your gut feeling, just apply another factor.
Kyle: 3% to the moon is a long way.
Screen: *shows 0.003% to the moon*
It’s so weird bc I use this method like all the time without realizing it’s like a thing. Like if my mom wants to know “how much have we spent on fast food this month?!!” I start figuring: a fast food dinner generally costs about $10 per person, as does the average Starbucks breakfast. Assuming we haven’t had anyone else visiting that means about $20 per meal. If our average weekly consumption of fast food in the past week was about 6 meals (including Starbucks breakfasts and fast food dinners) (she usually says this when we’ve had a month of copious fast food eating), and there are 4 weeks in a month, then we’ve had 24 fast food meals in the past month. If each meal cost $20, then we spent about $480 on fast food in a given month. Which totally tracks since I remember we once looked at a list of all of the transactions on her credit card for budgeting purposes, and we had in that month spend $400 on fast food. I’ve been doing this for ages and never realized it was like an actual method of estimating
Fun times, when I originally did my fermi estimate for the basketball problem I got a very similar answer to kyle's first guess (~100 games, 60 pts per team, 2 teams?). But then when he quoted the statistic for Stephen Curry getting 2,000 points a season I decided to use that, and went maybe there are 32 teams, each team has 5 players, and assuming Stephen Curry is about twice as high scoring as the average player divide all that by two, got 150,000. Goes to show that once you get a single nugget of good information you can use that alone to redo your estimate.
Fermi Estimate: all mathematical solutions are between 1 and Rayo's Number (or, alternatively, Large Number Garden Number)
17:00 Dump trucks no winder then 12 feet no taller then 14 feet (DOT regs) probable 16-20 feet long not counting the cab
Without checking and with showing your work how many videos has Kyle Hill uploaded to youtube?
Heh, I used this guestimation method a couple of weeks ago when a friend of a friend posted some slomo clips on Facebook of water balloons dropping on LEGO minifigs. She was wondering whether she could capture similar videos on her cell phone. Using a couple of things I knew (video playback is typically 30 or 60fps, acceleration of an object due to earth's gravity is 9.81m/s^2, the equations of motion specifically those of a constant linear acceleration) or things I could easily google (height of a LEGO minifig, 4cm) I was able to work out how long the original shot had taken in real time. From that I was able to work my way back to getting a ballpark figure of the frame rate the shot was taken in (~1500-3000fps) and then all I had to do was google some specs for cell phone slomo cameras: turns out some high-end ones claim framerates in the 1000-1200 fps range. So yeah, while a cell phone might not be near as detailed, capable or fancy as those Phantom cameras e.g. the SlomoGuys use, I figure a cell phone could get somewhere in the ballpark at least.
At the time I just thought I was feeding my inner nerd, not to mention feeling pretty chuffed about myself/the whole thing, I didn't know this was an actual thing, named after an actual genius to boot... TIL.
With the shark estimate, and I don’t know how accurate the final answer is, I would say the population of Great Whites is probably between 3-4K with 8 or 9 major areas with the greatest concentration, including California. Which would give me an estimate of 333 - 500.
I think part of the problem Kyle was having working on the question at the end was he forgot step 4.
With the hair, 5 mm/week doesn’t seem too outrageous if you don’t know how fast hair grows. But that’s 26 cm/year, which is over 10 inches. Kyle really should know that’s too big of an estimate. I estimated hair grows about 6 inches a year based on having long hair.
And with the basketball he started out strong with guessing 100 points a game per team, but didn’t do a reality check after saying there’s 100 games in a season. He was saying there 2 teams and they play each other 100 times a season. He obviously realized he missed something and went back.
But I always tell my students when they’re working on a problem or taking a test, does the answer make sense? If I tell you a rock sinks in water, then give your the mass and volume for you to calculate density and you give me a number less than 1, you have to know you’re wrong since you know anything less than 1 floats.
Robin everyday life. If I ask when the first automobile was invented and you say 1985, does that make sense? No. What about 1785? No. So maybe 1885 is more accurate.
I use fermi estimate usually when i am adding/subtracting/multiply or dividing bigs numbers in my mind