Exponential growth and epidemics

A primer on exponential and logistic growth
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/covid-thanks
Home page: www.3blue1brown.com
Excellent visualization of this kind of growth from Minutephysics and Aatish Bhatia:
• How To Tell If We're B...
Data source: www.worldometers.info/coronav...
Some have (quite rightfully) commented on how you shouldn't look at the R^2 of linear regressions on cumulative data since even if the changes from one day to the next are completely random, the totals they add up to wouldn't be independent of each other. Since the derivative of an exponential should also be an exponential, we could instead run the same test on the logarithms of the differences from day to day, which in this case gives R^2 = 0.91.
While this video uses COVID-19 as a motivating example, the main goal is simply a math lesson on exponentials and logistic curves. If you're looking for a video more focused on COVID-19 itself, I'd recommend taking a look at this one from Osmosis: • COVID-19 | Live Ask-Me...
Extrapolation xkcd: xkcd.com/605/
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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These animations are largely made using manim, a scrappy open source python library: github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with KZbin, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
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[@zerquix18]

"But if no one is worrying, that's when you should worry" sums it up perfectly

[@AvantGrade]

So memes or no memes? 😂

[@spyfox260]

Well, I'm not worried... >proceeds to die in 61 days

[@clucida]

Thanks for that video, I hope some of us will ask our governments to do more !

[@KLiCuk1]

you'll know when people are worried when the toilet paper shelves are empty.

[@petrabanjarnahor229]

@@AvantGrade yes memes

[@lapischicken]

"When no one is worried, that's when you should worry" Thanks Grant

[@McDonaldsCalifornia]

describes the state in Austria right now

[@TheRitualChannel]

That's a stock market/finance phrase too. Wise words. 🤗

[@ZomB1986]

I don't know if I should be worried that this is the first mention I get about the corona virus other than from hearsay and manual searching

[@quinnax]

So we shouldn’t be worried

[@Randive]

Everyone is worried meaning nobody should worry

[@antstraths]

3Blue One Brown: " This growth would mean Hitting 1 million cases in 30 days (April 5th)" World: *Hits one million cases April 4th Me: *Impressed yet shocked

[@Carolinagirl1028]

I just thought the same thing. Scary! Shows us what's to come ahead if we don't do everything possible to slow the spread. I don't want to see us hit 1 billion cases in another 2 months.

[@dungcheating]

10 million is coming

[@doaa7941]

I came back just to check how we're doing rn, not very great

[@ankithere423]

Get ready for 100million

[@fsxelw]

The growth factor seems to be decreasing though

[@theultimatereductionist7592]

The spread of a virus depends on two factors: 1) How dense the population is 2) How dense the population is

[@Ardjano234]

Hahaha

[@gmac8586]

So true!

[@gmac8586]

@xBirds Do you know where India is? It's bigger than a little piece of shore.

[@Sohlstyce]

3) how stupid people are Edit: I fit into one of the two.

[@andyyang5234]

@@Sohlstyce whoooosh

[@Scum42]

Inverse Tinkerbell Effect, then? The more people who believe COVID is extremely dangerous, the less dangerous it will be. When I first heard of this it was about driving safety: if everyone believes driving is dangerous, they will be more careful when driving, therefore making it more safe. But if everyone believes driving is safe, they will be less likely to be careful, therefore making it more dangerous.

[@futfan9092]

Reminds me of one of my favorite music lines: "I'm scared to death that I'll never be afraid"

[@xXkirkhammetXx]

In democracy, the more people believe their vote counts, the less it does

[@gileee]

@@futfan9092 Damn that's edgy

[@ASLUHLUHCE]

Interesting

[@za012345678998765432]

Exactly. we need to act early and effectively from an understanding of the *behavior* of the virus and pandemics, knowing that if we succeed it will seem like we panicked for nothing.

[@RobertHovakimyan55]

The day has come when the man who single-handedly taught us Linear Algebra is now trending on youtube.

[@5000subsnovideo]

Vishnu Kalluri exponential growth is taught in Algebra 1, or sometimes in some courses, in intermediate algebra.

[@pkgamma]

Guy taught me an entire semester worth of Calculus 2 in a day before my final exam last year. True legend indeed.

[@sublimetrance]

I agree. This is probably one of the best if not the best math channels on youtube.

[@duncanw9901]

@@sublimetrance flammable maths is good for more specific, more frequent content. And Fematika is good for exercises in humility; having a 14-year-old teach you category theory is quite.... an experience.

[@robin9793]

A God among mere clickbait

[@st-li8ez]

I'd like to point out that 3 weeks ago, this simulated curve showed us passing 1 million total cases on April 6th. It's April 2nd and we just did so. That really shows the power behind the exponential and how closely an epidemic follows it.

[@HiFisch94]

Came back just to write this. Back then the American growth wasn't relevant for the curve. They made the curve ascend faster

[@oteatimeo]

@@HiFisch94 not all states practice social distancing so exponential growth will continue longer. Also, China, N Korea, Iran,... are hiding their "number".

[@andrewdojlido7940]

@@oteatimeo My roommate is from Iran. He has had two family members succumb. The government there is not being forthcoming nor do they have the capacity to deal with it in many regions he said.

[@oteatimeo]

@@andrewdojlido7940 My condolences to your friend's lost and God knows the Iranian people have suffered too much already. No words can ease the heartache of lost Loves, the passing of time perhaps.

[@wieysw2907]

oteatimeo and USA

[@richardgreen7225]

"If no one is worried, that is when we should worry."

[@thaDjMauz]

Haha thats such a typical thing! It's like that with meditation for a lot of people; the less you want to do it the more you could use it.

[@feloniousgru8964]

Ah yes, November 2020 in one statement

[@pendulousphallus]

I'm just impressed he got this shot, editted and gorgeously animated in just two days.

[@noonoox12]

Interestingly, he actually wrote an interesting engine to automate the animation process of his videos

[@undisclosedmusic4969]

When intelligence and Python come together, no feat is out of reach...

[@0xCAFEF00D]

@@undisclosedmusic4969 Except performance. And consequently energy efficiency. And really if you're doing anything significant you're relying on a good base of libraries written in other languages.

[@0xCAFEF00D]

@@vesui2130 Of course. I'm just a little bit sick of how people attribute so much to python. Its a fine language and ecosystem but the credit should be shared more.

[@dyf123cxe]

" if people are sufficiently worried, there’s much less to worry about, but if no one is worried, that’s when you should worry." I fully agree with that. Pay attention, gentlemen.

[@neilmcmahon]

women don't need to pay attention ?

[@rasibnadeem8519]

@@neilmcmahon women don't exist

[@neilmcmahon]

@@rasibnadeem8519 With a name like yours, I would think that you actually believe it.

[@themadman300113]

Neil McMahon racist much?

[@neilmcmahon]

@@themadman300113 Are you not going to comment on the sexist comments or do they not offend you. I will tend to be offensive towards people that are being sexist. Eye for an eye, right ?

[@Mavhawk64]

Looking at this almost a year later and realizing how accurate he is...

[@wamsang7818]

"Everything we do before a pandemic will seem alarmist. Everything after will seem inadequate."

[@gmac8586]

I love it, but I see quotes. Can you tell us who you're quoting? Thanks.

[@jonk8893]

Lit

[@lawrencemccreery3451]

Still seems alarmist

[@vlogbrothers]

I needed to see this video today. So do millions of others! Helpful, concise, unalarmist, and a good lesson in exponential growth to boot! Thank you. -John

[@johnchessant3012]

Hi John!

[@iwanabana]

And they'd probably would appreciate a small donation somewhere because YT is reaaallllyyy trigger happy with demonitizing every video on the Chinese Coronavirus.

[@PJsPhotoJar]

hi John!

[@NoActuallyGo-KCUF-Yourself]

DFTBA

[@AlexandraDuranton]

John "I don't math" Green watching 3b1b? Hats off. Seriously though, when I think of "math" and "John Green" together, old vlogbrothers videos come to mind, specifically the ones involving either phone calls to Daniel Biss or frustration towards high school John Green. As weird as it sounds, I remember being immensely proud when you, a grown man whom I've never met, announced that you had started taking some kind on online geometry class despite having previously had and unpleasant experience with the subject. You've come a long way, John, and I'm glad to see you here. All the best, Alexandra

[@thirukumaran1318]

"If people are sufficiently worried, then there's a lot less to worry about. But if no one is worried - that's when you should worry" Brilliant summary of the exponential model.

[@Czmlol]

The same can be said about technological singularity that we are recklessly galloping toward with no stop button or reset switch. The one greatest vice in the entirety of humanity is the profound lack of understanding of the exponential function.

[@z4m01]

My country in a nutshell, the government is zero worried and treats the population as feared children.

[@ASLUHLUHCE]

@@Czmlol Dude that's so profound, you should write a book

[@erik-ic3tp]

@@Czmlol, True. Exponential growth's so alien to most people. Also, what's wrong with the Singularity per se? I'm just curious. :)

[@jeetadityachatterjee6995]

@@erik-ic3tp the singularity (in Thai context I think ) is when ai becomes so powerful that it can almost mimic a human mind in many ways. This has profound impacts both ethical (as you have essentially created a sentient being) and physical as this ai MAY not conform to our way of thinking. This can lead to its spread and maybe some bad stuff along the way. It's pretty cool and also very scary.

[@JeffGeerling]

"If no one is worried, that's when you should worry" 🤔 Applicable in many ways in many situations!

[@howedaddy6122]

V

[@4a14hugoho4]

right

[@stevenverrall4527]

The converse is also true...

[@mustafamalik4211]

Now whenever your kids ask you where they will use math in the real world, you show them this video.

[@TheEshanDas]

First slap them across the face for asking such a stupid question :D

[@thepro8447]

@Rajeev Vij that doesn't change the fact that it's still child abuse though

[@guitarslim56]

I bet you anything that the college kids who are right now partying on the beach in Florida are lousy at math.

[@mustafamalik4211]

​@@guitarslim56​There's a virus outbreak right now, what kind of idiots would party now?

[@mustafamalik4211]

@Hamza Hussain Yeah, but coronavirus doesn't stop when college's close.

[@jasonb4566]

Viral outbreak appears. People: "I guess I will finally learn exponential growth mathematical models"

[@phandinhthanh2295]

Calculus students be like: hold my beers!

[@Joelo26]

I haven't seen this topic since college, more specifically, since I took calculus which by now is ancient history.

[@crazyhq270]

@@phandinhthanh2295 Hold my partial differential equations.

[@jayclyde6045]

Do you guys and gals remember those days sitting in math class and you had that one person ask, "When do I ever see the point in using this in real life?" That person might be trying very hard to get brushed up on that topic of math right about now.

[@itchykami]

I wish people learned about exponential growth models, instead of parroting 'this isn't even the flu' at me every time I suggest being at least a little ready for trouble.

[@mapletreemon4834]

My man really just took the second derivative of the coronavirus

[@darian3788]

this is a lot funnier than it should be

[@David_F97]

😂

[@fahezunahmed3605]

And it's positive.

[@ertrupik670]

uuuuuuhhhh

[@jonahpoulard7674]

it's not a derivative he didn't differentiate but close and it made me chuckle x

[@WonieSong]

Everytime I watch this channel’s videos, I am awestruck by their qualities. I feel even lucky to have found this channel. Thanks for another quality lesson!

[@mokumoki]

Looking at 3:10, he is drawing the line using cases recorded outside China. We technically haven't reach 1 Million outside China yet, as the current 1 Million cases included 80k cases in China. Therefore, 3B1B prediction is a lot closer than what we think: 1 Million cases outside China on 5 April, because now we are 80k off the 1 Million mark, which we will reach tomorrow.

[@presidentmegtawma6845]

The world reached 1 million cases (actual) before the first case was confirmed outside China. The CCP is just lying.

[@Obi-Wan_Kenobi]

Fantastic. My two greatest fears coming together. Disease and Math.

[@b.clarenc9517]

Did they cancel each other?

[@prodators301]

General Kenobi !

[@henryshaw5208]

😂

[@elvijsk]

This is great :)

[@deren2001]

Lol!

[@georhodiumgeo9827]

So my buddy was driving us around and he ran a red light. I said “You just ran a red light! That’s dangerous you will get us killed.” He said “Don’t worry my brother drives like this all the time, it’s fine, people will stop for you.” A bit later he pulls up to a green light and stops. I said. “You just stopped at a green light why are we stopped at a green light” he said “You gotta be careful, you never know when my brother is coming from the other direction.”

[@alazrabed]

Indeed, that's why I go only when it's orange.

[@MrGilRoland]

I feel like there is a moral of the story there, somewhere, but I’m not getting it.

[@alazrabed]

@@MrGilRoland Look into the orange light and you shall see it.

[@moodi4567]

MrGilRoland 😂😂

[@DZairCuisine]

I like this approach in life. 😂😂

[@sumsamullah589]

3:06 "if the present trend continues we will hit a million cases in 30 days" Turns out the trend has continued!

[@infopentrunoi801]

false positives...

[@PurushNahiMahaPurush]

This is one of the best videos about covid 19 spread I've seen. I saw a few from Thunderfoot and his videos come off as a bit too "doomsday" ish. The last thing you need now is panic and fear. The key takeaway of this video is how social distancing and washing your hands, even if it looks futile, can drastically reduce the spread of the disease and buy us time until we either ramp up medical facilities or find a cure.

[@citrine615]

This analysis makes a very strong case for the importance of scientific and mathematical literacy. Specifically, about the fallibility of gut feelings.

[@JonathanAnimate2]

I don't think people thought it would spread seriously outside of east Asia. And the numbers coming out if China were not of global significance. Of course we now know China's response was superior to most nations and we're now looking at potential future death numbers we've only ever read about. Richer nations, despite their own crisis, I hope will find a way to provide resources and expertise to the poorer nations. We can be thankful that they'll mostly by be hit last, when more will have been learnt.

[@bethyjenkins]

Makes me think of this book I've bookmarked to read - All Things Being Equal: Why Math Is the Key to a Better World. I just read the intro and it just made the case that many kids/people are intimidated by math, it's usually easier to grasp and more interesting than one would assume, and we'd all make smarter decisions if we were more mathematically literate.

[@basetoace3951]

​@@bethyjenkins Hey! Sorry to bother you but i'd like to read that book too! Can you provide me the link? Thank you in advance

[@anttikarttunen1126]

Also, I would make it compulsory viewing for all these pundits who wrote (and some still write) these clickbait stories, how "During the time corona has killed _just a few hundred_ people, X people died from cause Y", where Y is something like falling from the ladder, or drowning in your bathtub.

[@bethyjenkins]

@ace of base here’s the amazon link (I think it’s on audible too for less $): www.amazon.ca/All-Things-Being-Equal-Better/dp/0735272891 I was able to read the intro for free, but I can’t remember where (maybe the publishers website, not sure).

[@patrickgunning1024]

what's so frustrating is that people don't have a concept of sufficiently worrying about this. They're either buying gallons of hand sanitizer or convinced it's some media conspiracy to get you to buy hand sanitizer

[@ashannoweria2855]

So what should we do

[@patrickgunning1024]

@@ashannoweria2855 I don't have any authority here but listen to health experts. Stay home from work/school if your sick, wash your hands, avoid physical contact with strangers, don't touch your face. Respect the fact that while you probably will not become seriously ill that many others will die from this.

[@Abdega]

If they only buying cleaning products *NOW* they nasty and haven’t been washing their hands

[@MrKnutriis]

@@Abdega Damn right. It's too late to start washing your hands now.

[@idahagglund524]

How is it too late? If you grab a handle in a public space, and then use hand sanitizer to kill any potential virus on your hands, how's that a waste? It means you won't be infected and thus can't spread it to others around you for up to two weeks before you show symptoms and hopefully have the sense to quarantine yourself at home.

[@tonyrahme96]

We’re just 5 days from April 6 and already the total cases is about 1 million this man predicted the future

[@oliviashen1060]

Coming from 7 months in the future, I have to say... he was right to be concerned

[@okbro3524]

Yet, he was wrong on many other things

[@nukexplosion6679]

@@okbro3524 like?

[@KM-nt9nj]

3 months ahead of you, the end is near :)

[@matrixyst]

​@@KM-nt9nj 6 months ago: "We're almost out of this!" Antivaxxers 6 months later: "NO YOU AIN'T"

[@yomer355]

I mean the world pandemic was declared around those days, it's not like he was among the few who were concerned, everyone was.

[@3blue1brown]

While the intent here is to give a lesson on exponential and logistic growth as general phenomena, with epidemics as a timely case study, there are a few notes worth adding when it comes to epidemics themselves. Probably the most important, mentioned only as a small on-screen note, is that these models should account for the amount of time someone with the virus remains infectious. Those who recover (or die) are no longer able to spread it, and so don't factor into the growth equation. The faster the growth, the less this matters, since at each point on the curve most people with the virus will have only contracted it recently, but especially in the long run or with slower growth, any realistic model has to consider this. See this followup: kzbin.info/www/bejne/namkkoJop9iXf9U The other factor, which I was hesitant to even get into here, is the extent to which reported cases reflect real cases. Generalizing away from epidemics, though, the key upshot is to be aware of phenomena where the rate of growth is proportional to the size of the thing growing. Compound interest, technological progress, population growth, and many other things fit this pattern, and it's shocking how bad our intuitions can be at recognizing what it means.

[@aleksitolonen2274]

This video was well explained like always.

[@lckite9823]

3Blue1Brown thank you! I was about to ask, what if someone recovers? But I get that the point is more to explain exponential growth than to make a good corona virus model. Thank you again for the great video

[@thebeansareonfire]

Dont worry Grant we got the general message. You explained it beautifully through Mathematics

[@geggam]

@@lckite9823 I havent heard people are building immunity to this. Are they immune when they get it or is it like the flu and you get it again ?

[@know1374]

We could create a supervised learning model using R (as it contains a detailed package just for the epidemic) that includes all the constraints and features you mentioned then statistically carve it (adjust values like p and r², adjusted-r², and other statistic summary) to meaningfully predict what the unholy virus could have in store for humanity and how we can tweak phenomena to make it meet it's maker.

[@ASLUHLUHCE]

Moral of the story: Scare everyone into isolating themselves and always washing their hands

[@yume3480]

Actually that's what the TV does :D at least in my country

[@Echteseele]

That's what government is doing right now in Italy, basically the message is: stay at home! and in case you have to go out, stay 1 meter far from any one else

[@misakamikoto8785]

There's a reason why China lock down 50 million, even they're a country that like to downplay everything.

[@mikebolton2388]

You mean live with uncertainty and practice good hygiene

[@lewiszim]

We've already reached that point here in Seattle. There's very little traffic on the road. Most people are staying in their homes. People are thoroughly scared.

[@shadyganem5448]

I Love how math makes the most complected processes in the world predictable.

[@sander_bouwhuis]

I loved that self-fulfilling (or self-defeating in this case!) sentence at the end! ("The only thing to fear is the lack of fear itself")

[@DeclanMBrennan]

"Let's reduce infection so we can see that inflection. "

[@thegreaterconundrum]

👏

[@cinemarat1834]

I can see this being a rap

[@DeclanMBrennan]

@@cinemarat1834 :-)

[@mr.champion7304]

+1 for the great pun

[@Quixote1818]

Already over 2 million views in 3 days. This video is going viral! No sign of an inflection point yet. :)

[@ewerninghaus]

Quixote1818 3.3 million views in 6 days. Inflection it is. Unfortunately with only 2 data points it is very risky to make any extrapolation.

[@SherwoodBotsford]

But it HAS passed it's infection point

What about abacaba

[@kevinemery9595]

No sign of an inflection point on the virus' spread yet either. The 21,395 figure at 0:40 is now over 200,000, two weeks later.

[@adyear3168]

This video is going viral without an inflection point so far. Ha ha. Both knowledge and humour help, even in a pandemic, even while writing in a precautionary 14 day self quarantine. The absurdity of denial we have experienced in the preceding 2 months is also helped explained by this mathematical model, to a point. Japan at time of writing is still not canceling the July Olympics and Mitch McConnell is predicting a fabulous 4th quarter for the economy this year. WTF??? I will applaud a ‘miracle’ treatment or safe vaccine regardless. If you dare to laugh further, Norm Macdonald dared to to due a Coronavirus comedy segment, funny & risqué (about 5 min with language disclaimers): kzbin.info/www/bejne/Y6TOcmd9nbuLbc0

[@adrianoaxel1196]

Your videos are of an amazing quality. Congratulations not only for the edition effort but for the mental organization of the ideas. :)

[@RealPi]

As a maths prof, I often show this video to people interested to understand in a rudimentary way why they need to wash their hands and practise social distancing. I applaud your work and contribution, thank you!

[@josephjoestar77]

@channel break maybe they meant this channel's video, and not this particular video

[@RealPi]

@channel break How come "often" implies "for years"? I recommend the channel to a number of people and in particular I have been showing this video daily (since it came out, obviously, not..for years) to many non-students who do not understand the concept of exponential growth and it has led many of them to understand the importance of social distancing and personal hygiene. As this was due to the nice exposition of this video (something kept throughout other videos on the channel) I figured I would say thank you.

[@jeffsuess377]

Beautiful. I'm a math teacher who will still be in school on Monday (my province in Canada is slightly nuts), this is getting shown to all classes. You calm voice is a big help.

[@randomrandom450]

Math to the rescue :)

[@iamapokerface8992]

Your*

[@randomrandom450]

@@iamapokerface8992 go away

[@ryanscholz_]

Queensland Scientists have found a cure, everyone can relax

[@IStMl]

@@ryanscholz_ No

[@TheAgamemnon911]

Experts: Avoid crowds. Me, procrastinating all week on KZbin: Already 1 step ahead.

[@ubivermiscerritulus195]

Same lol. Everyone told me to get out more but now what are they saying smh

[@linapalacios4729]

Same

Can't lose your life to a virus if you don't have a life to begin with. Checkmate covid-19!

[@MrKnutriis]

@ lol

[@MrKnutriis]

LOL

[@klauskraywinkel4983]

... you brilliantly demonstrated that mathematics is indeed a life science. Thank you!

[@andyisdead]

math saves lives

[@okbro3524]

Funny how wrong he was

[@paulmccartney8293]

@@okbro3524 wrong?

[@unkindleddruid4565]

@@okbro3524 wrong?

[@jensmalzer6344]

@@okbro3524 wrong?

[@TamaraTkacova]

Swiss scientists used your video to spread awareness and help people understand the exponential infection rate, and I‘m so proud of your channel as well as them for providing clarity in this time of chaos^^ as always, great video thankyouu

[@apoorvemishra5102]

"When no one is worried, that's when you should worry", First video from a series on game theory :)

[@TheExoplanetsChannel]

Oh

[@klanowicz]

Oh

[@klanowicz]

It will be bad

[@cadekachelmeier7251]

It's an example of the reverse tinkerbell effect. An idea that if everyone believes it, it becomes not true. And is only true if nobody or few believe it. Other examples are the idea that your vote matters. If everyone believes it, everyone will vote and your vote will matter less. And if everyone believes that cars are safe, then they will drive more recklessly and driving will be less safe. The other side of the coin are ideas that are only true because people believe them. Like that money has value or the rule of law.

[@neloru1122]

I'm skipping my school's online math classes to watch this online math class

[@geomochi4904]

@repetemcfly bUt yOU cAnT sPReAd tHe viRUs oNlINe

[@nanigopalsaha2408]

@@geomochi4904 But you can spread other viruses (viri?) online.

[@user-po9yn4ni4u]

@@geomochi4904 there is a virus called stupidity which can spread online

[@stumphole145]

@@user-po9yn4ni4u LMAO

[@geomochi4904]

@@stumphole145 well I guess no-one can tell I was joking

[@guardingdark2860]

Firstly, well done as always. Way to turn something like this into an interesting math lesson. Secondly, I feel that I am sufficiently worried, and the empty shelves at my local supermarkets suggest that my community probably is, too; my main concern at this point, then, is "is there such a thing as being TOO worried?" Namely, I am concerned about depleting resources that might otherwise be better used a bit less frequently so as to last longer and hopefully wear out the bulk of the exponential growth. The one that immediately sticks out in my mind is hand sanitizer; I work in retail, so I see a lot of people coming and going all day. As such, I have been trying to wash my hands whenever I get the opportunity, and using hand sanitizer every 10ish transactions. However, the unsurprising fact that supplies of hand sanitizer are suffering a dip right now makes me wonder if it might behoove me to reduce that to, say, every 20ish transactions (or once every hour or whatever) in the hopes that I am still cleaning often enough, but also not overusing what has suddenly become a precious resource. I have not seen any specific recommendations on this, and anyone who has seen them, I welcome the information.

[@rustoo3823]

What a wonderful video related to the current situation :) I hope that 3Blue1Brown works on a sequel to this!

[@ephremadmasu2279]

"True exponentials essentially never exist in the real world. Every one of them is the start of the logistic curve." was an aha moment for me.

[@densely]

Exponential or self-reinforcing behavior exists in the real world. It doesn't carry on forever.

[@AA123TD]

Well ut could be that we will all die so that would definitely end the curve. jk 😉

[@joshua43214]

@@densely To the best of my knowledge, *all* biological growth is logarithmic. Exponential is by definition unbounded, and thus carries on forever. Not sure what you mean by self-reinforcing in this context.

[@user-xs9oo9gc7u]

Not really, power level in animes or games grow exactly exponential.

[@unoriginalusernameno999]

Bacteria exhibit true exponential population growth. Why do you think there are so many micro-organisms? But human population growth is not a true exponential.

[@sebthealiens]

"Australia is about a month behind" is the most unsettling thing I've heard in a while

[@emceeboogieboots1608]

@serendipidus1 Yes, you would think we had an outbreak of diarrhea rather than covid19 ....Sheeple😒😒

[@LeeCoangSee]

-COVID- WHCoV✔

[@kimba381]

@serendipidus1 It's the most ridiculous thing I've ever seen! of all the things to panic about: toilet paper for god's sake. I am disturbed that I live in a country of morons

[@edwardk3]

Travelers law: in every hostel in the world right now, there is somebody from Australia.

[@izzygarnelo]

@dianna k You mean dying.

[@pierrerust2423]

Excellent explanation : clear, well structured and illustrated, and right to the point ! Well done ! Every scientific and mathematical popularization should be presented like this.

[@ricardogonhin]

And this is why you’re my favorite KZbin content creator!

[@iwillfreezeyou]

I’ve been trying to explain this to my friends for DAYS!! Now i’ll just have to link them for an even better and simpler explanation

[@ZackLee]

I tried to explain it to my friends, but they like to pretend they understand math and it ends with "data from the government cannot be trusted"

[@nuklearboysymbiote]

@@ZackLee that last bit is true though

[@IloveElsaofArendelle]

@Sjwaria Law I stopped convincing my friends around. I am prepared, I just ordered my 5l isopropyl alcohol to mix my 75% Vol. Solution

[@ZackLee]

@@some_developer nope, they are pretty set on not worrying about it. So I just stocked up on stuff without them

[@ErraticMagics]

"When the world is filled with red lights signaling danger, the world is safer than usual. But when it's filled with green lights signaling safety, it creates a place more dangerous than anywhere." - Oshino Ougi

[@fran6b]

Nice quote!

[@CHEpachilo]

NisiOisiN, actually .

[@fabiovezzari2895]

Like in 2008

[@hesiod_delta9209]

I like to call this the paradox of risk and caution.

[@QuakeGamerROTMG]

This was the last place I expected to see a Monogatari quote today

[@mokrodrigues4515]

This is my favorite youtube channel! Thanks for the videos!

[@ralfbaechle]

I always liked your calming voice and style of presenting things. But to no topic before this was more fitting that the growth of the pandemic. Thanks!

[@SocksWithSandals]

Haha "The only thing to fear is the lack of fear itself" That's worrying because I wasn't worried!

[@know1374]

Yeah, what

[@v44n7]

You have to be worry enough to know if your hand are clean or if you toched your face the last minute. More than that no really, avoid crowds. Just look at this video , If we all do a little bit we can reduce E & p. If we do that long enough, people infected will either die or get recovered. So E will naturally go down with time. We have do worry enough to not get infected so we can prevent other from getting infected from us long enough for this to peak faster (Inflection point), so we reduce our chances to get infected each day.

[@randomguy263]

I'm still not worried.

[@sadigov]

This is similar to a famous quote by a former US president Leohardo DiCockrio.

[@zmartkooky244]

Now you are worried that you weren't worried. Problem fixed.

[@sufyaansyed8057]

Corona and math. Wonderful way to start my Sunday

[@PAULSWorld131]

Everything in the universe = Math ;-)

[@ruiverissimo2864]

Taking into account what I learned with this video about math, about the covid19, and hence about how math applies to life, I can only tell you one thing: thank you. I'll chat with my kids tonight about this video. Bless you.

[@joemama62]

Thank you, a great explanation. I have been trying to get people to be sufficiently worried without panicing!

[@billschlafly4107]

@8:30 "If no one is worried, that's when you should worry". Now I'm really worried.

[@matthewgillespie2835]

But many people are worried, perhaps overreacting. Or maybe it’s just that there’s selective bias regarding my observation of how worried everyone is, because I spend much of my time online.

[@AA123TD]

@@matthewgillespie2835 Seems people in the US are not worried like other places. A lot are calling it fake news and that more people die from the regular flu than this virus. CFR is 5% in Italy right now. That is quite concerning.

[@Marco-zt2jj]

@@matthewgillespie2835 by reading stuff online I feel like most people are downplaying it tbh. Yes there's no need to panic but it's not just a common cold either. If your reasoning is that most people will recover on their own and just a small fraction will die then people shouldn't have been worried about the spanish influenza either, not to mention the fact that the main problem of this virus is the amount of people who need hospital treatment, ICU etc, and if numbers get too high there won't be enough space for everybody in hospitals. Why do you think they built hospitals in 10 days in China? Right now hospitals in nothern Italy are overwhelmed, doctors have to spend most of their day at work, they're recalling retired doctors, "promoting" medicine students etc because there isn't enough personnel, and buying new equipment, the problem is that if you dare to mention this kind of stuff people accuse you of fear mongering Yes, most people won't die because of this virus, and panic is counterproductive, but first of all if you have grandparents you shoud care about them because they're in danger, and same thing for immunosuppressed people (which is a reason why vaccines are important as well), or even if you have 60yo+ parents or relatives as for 60-69yo there's a mortality rate of 4-5% iirc (correct me if I'm wrong), and most importantly, even people who don't die may have to spend weeks in a hospital because they're not able to breathe on their own, then there's potentially permanent lung damage and so on, so I repeat, no panic but you still have to take it seriously and try to collaborate to slow down the spread, this is neither just a regular flu nor the common cold. In Italy the government had to adopt stricter laws because lots of people didn't care and kept gathering in crowded places and similar stuff so that the virus keeps spreading exponentially, and I feel like most people in the world still have the same attitude of those italians who kept minding their own businness causing the virus to spread

[@NoriMori1992]

@@AA123TD That's fascinating. It never occurred to me that there might be areas where people aren't very worried. I live in the Greater Toronto Area, and in my city many stores have completely run out of N95 masks, hand sanitizer, and antibacterial wipes. The store I work at has had N95 masks on backorder (meaning the supplier itself has run out) for weeks (and I've heard other stores are in the same boat); we're completely sold out of hand sanitizer and don't know when more will come in; we keep running out of antibacterial wipes; and yesterday the shelf of disinfectant wipes (e.g. Lysol) was almost completely empty. What little disinfectant wipes we have left, we've started keeping behind the counter with instructions to sell only one per group. A few weeks ago we had multiple people a day asking about N95 masks; now that everyone knows they're gone, it's all about hand sanitizer. A customer from Toronto told me he can't find any there either; he came to my city to look for some, because he assumed that there wouldn't be as much panic buying in a smaller, less dense city. Some stores - the kind that people wouldn't think of, like bath and beauty stores - still had some hand sanitizer as of a couple days ago, but who knows how long that will last. It's not like people are panicking in the streets, but they're clearly worried.

[@ishworshrestha3559]

Jik

[@filippomioli8937]

I'm from Italy, our contry is doing everything possible to isolate the hotspot where there were the first infaction. Today we have a few region were people are obliged to stay at home and move only to work or buy food. School and university are closed in all the country. Yesterday I was just thinking about the exponential and logistic growth of the virus and I was triyng to explain to a friend of mine how the restriction imposed by our country has the goal of lowering the asymptotic limit of the infected. Unfortunately, I'm not a mathematician and I didn't have the skills to plot a cool graph as yours. So, thank you so much. I'm gonna show this video to all my friends. Remember this:" You find it only if you search it". In Italy we have made hundred of thousand of swambs, and found only 5000 infected.

[@shubhammaurya3671]

Yeh, that video explain a lot. Stay safe

[@The-illuminated]

I wish i lived in Italy then.

[@MrKnutriis]

Knowledge is power - I hope your friends will watch.

[@thyros_]

Im also from Italy

[@vincenttse3167]

Stay safe dude!

[@jonathangladstone1790]

This is excellent. I'm sharing the link with two groups of students I currently teach at Georgian College, in Barrie, ON. One group is taking Mathematics for Data Analytics with me as part of a post-graduate certificate in Big Data Analytics; the other is taking Contingency Planning & Disaster Recovery as part of a post-graduate certificate in Information Systems Security. Thanks! Ironically, I'm one of four children - three blue & one brown - from two brown-eyed parents.

[@pluribus]

“The greatest shortcoming of the human race is our inability to understand the exponential function.” ― Albert A. Bartlett

[@mastersuper7149]

Kids: NO MORE SCHOOL! YEAH! 3Blue1Brown: Hey, learn the math!

[@TheTenthBlueJay]

Let's be honest, all of us are nerds

[@nothingtoseehere975]

I am in middle school and i still think that the unexpected break is extremely bad because the summer break is going to be cut short

[@abisarwan7682]

😂😂😂😂😂😂😂😂

[@Yobs2K]

@@TheTenthBlueJay lol no. You don't have to be a nerd to be interested in this kind of things.

[@mhm7604]

Schools closed for you?

[@aurkom]

People: "Panic" 3Blue1Brown: "Pause and Ponder!"

[@TheExoplanetsChannel]

.

[@stelley08]

Only idiots panic because only idiots watch the mainstream media propaganda, i mean "news"... 'its 6 oclock, heres what we want you to know'...

[@nigels9077]

We dont need to be panic but sufficiently worried

[@stelley08]

@@nigels9077 dont worry, be happy. Deal with things as they come to you, worrying is like being on a rocking horse, you go back and forward but dont get anywhere.

[@DR-54]

@@stelley08 The main worry about SARS-CoV-2 is that we don't know the magnitude of it's spread at the moment so we don't know if we should or shouldn't be worried. 3 TSA workers were diagnosed with COVID-19 and TSA workers touch a lot of people, it's likely that now thousands were infected from that airport alone.

[@markvyber2458]

Man, have I ever told you how great your videos are Thanks

[@sharxbyte]

We're watching this in my Calculus class in 2023 and the projections in hindsight are both affirming and frustrating.

[@cold_static]

This might be your last chance to learn about exponential functions, so watch closely!

[@ScormGaming]

Boys & girls, it is now or never to learn about the expression of the Normal law !

[@jarediannudalo6074]

😂

[@blackbird4062]

The coronavirus is just a flu

[@cold_static]

@@orangecapy9494 I think the one being ridiculous is you, as you clearly understood I was making a joke, yet somehow claim I am "ignorant" at the same time. To make it absolutely clear to you: Yes, I understand that this virus is "not that bad". I was being dramatic for comedic purposes. You are a twat.

[@SpocksBro]

@@orangecapy9494 The mortality rate currently is still around 1-5% in well developed countries where good medical care can be provided. That's not like a flu, that's worse by a an order of magnitude at the very least. Further more there currently is no vaccine against it and there won't be for quite a while. The irony here also is, that after watching this video, you should at least have realized that at the current growth rate, many hospitals are going to be overwhelmed by the influx of severe cases. And it really doesn't matter if only a small percentage of the population experience severe illness due to certain preconditions or old age in this case either because the severe cases need extensive medical care and no hospitals are going to have enough machinery to provide that. I'm not here to predict dooms day but you seem to be wearing rose tainted glasses.

[@schmoyoho]

THANK YOU, i always wondered what it was called when exponential growth slowed down, i finally feel like a scholar 🙏💖

[@RyBrown]

schmoyoho haha how does your comment only have three likes?

[@multiwonderrr]

Notice me senpai

[@imranraja6156]

You: We should be worried. Your neighbours: We shouldn’t be worried. 3Blue1Brown: We should all be concerned.

[@sunitasasi6452]

Exactly.. Concern is the actual 'WORD'

[@dddmemaybe]

@@sunitasasi6452 Don't be scared. Be educated ;)_

[@cappyodi9221]

Thank you so much for this video. I have been trying to explain exponential growth, inflection point, logistic curves, and logarithmic scales to people nonstop.

[@immortalized_onion]

Procrastinating studying Maths by watching maths. "gEniUs"

[@svnshne1415]

....What a mood. (Exactly what I’m doing rn.)

[@-dialecticsforkids2978]

not like this is real maths

[@olofpalme3662]

- dialectics for kids wtf do u mean this is not ”real math”??

[@-dialecticsforkids2978]

@@olofpalme3662 u do exp function @ school, not @ uni

[@olofpalme3662]

- dialectics for kids how does that not make it real math??? does that mean 1+1 isnt math just because you dont do it at uni?

[@Felixkeeg]

"True exponentials essentially never exist in the real world" Economists: " *LALALA* I CAN'T HEAR YOU"

[@drdca8263]

Felixkeeg Yeah, I hope people are working on good mathematical models of how to do economy when production can’t grow much more. Much of it should still transfer over I think, but I would imagine passive investing would become less effective? And like, interest rates would probably go down. (... uh, interest rates are already low..., but I don’t think we’ve hit a growth wall yet. I suppose I mean that interest rates would go down and stay down?) Hm.

[@WestOfEarth]

note the use of the word 'real'. Look at Wall Street. So much of stock market growth is based on thin air. And think about this, given what 3B1B has outlined here. Indefinite exponential growth is impossible even in Wall Street's lala land. Market corrections do little to slow this growth, a growth that ultimately ends in utter collapse.

[@marcagray]

Central bank: “Hold my quantitative easing!”

[@groforoctavioarmasvega3201]

You're safe with Braum

[@drdca8263]

WestOfEarth I think it possible that in nominal prices, could continue exponentially indefinitely (as long as it continues to exist) so long as inflation is exponential decay as well. But in terms of real value and production, no, because thermodynamic limits.

[@justaperson1812]

grant all the steps in this explanation are so beautifully elegant. thank you

[@mirkono]

I was waiting for you to create this. Thank you !

[@wshtb]

The U.S. gov: there is no exponential growth of COVID-19 in the U.S. Also the U.S. gov: ... because we only have linear growth of test kits!

[@codybarrett4672]

not really but ok

[@maxsolo2652]

True

[@dongyufan8049]

"If people are sufficiently worried, there's a lot less to worry about. But if no one is worried, that's when you should worry. " That's the point I'm always trying to make to all my friends (who believe it's not a big deal)!!! Thanks!!! It's a fantastic video!!!

[@tjw2469]

Dongyu Fan 我身边除中国留学生之外的所有同学都认为我大惊小怪了

[@cowl6867]

I think you took it the wrong way

[@Zeero3846]

That doesn't justify panic though. Worrying != panicking. Don't take buy out your local stores' supply of precautionary goods. That's panicking, and you're limiting everyone else's (including hospitals that still have to deal with the regular diseases) ability to take precautions, making that number worse.

[@danielornelas3520]

Dongyu Fan yeah... you are taking this the wrong way as is everybody else! #Bealertnotanxious wash your hands... leave supplies for everyone else and don’t panic!

[@dongyufan8049]

@@danielornelas3520 The point is exponential growth can be horrible but it can be controlled by lower the growth factor. eg, wash your hands and avoid sick people. Right now, people are not sufficiently alert, that's when we should be worried.

[@Higginz1991]

Like almost anything you can think of, too much of anything can be just as harmful as not enough. Worry too much and you crumble, worry too little and you put others at risk. Thoroughly enjoyed this video.

[@amerryatheist]

As a math prof, I love your video 3Blue1Brown ^.^ I am going to show this to my calc students to explain exponential growth.

[@7head7metal7]

3:40 "And as always, there is an XKCD for that" :D

[@trumpetperson11]

I don't know how you do it man, but you make this stuff so interesting. Like I would say that I like math, but I can even have a hard time paying attention in my lectures, yet your videos always breeze right by even when they are about similar topics. I don't know if it is the visuals, your smooth tone, or your scripts, but keep it up man, love the content.

[@StevenTorrey]

One of the better & clearer explanations for exponential growth.... It really is a 2nd Semester Algebra 1 problem... Very simple algebra.

[@LePerlashez]

What we need the most right now is to be rationnaly worried. Btw great job, with all those explanations, it has made things much clearer.

[@Legominder]

Take home message: Decrease daily infection rate by 2/3. In 2 months: 250 times less people infected --> So minimize ANY exposure as much as possible. Exponential growth is just sth. we don't have any intuition for. Always surprises me again. We only think linear. And I say that as a physicist;D

[@crediblesalamander8056]

Modelling epidemics was my favourite part of our course on recursion, I'm glad you covered it :D

[@SybotLV5]

What I like about recursion you ask? I will tell you in a second. What I like about recursion you ask?

[@sayamqazi]

@@SybotLV5 translating this sentence to a language different from what it is written in will reveal what recursion is.

[@ScormGaming]

​@@SybotLV5 LINUX ? Linux Is Not UniX ? Linux Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX Is Not UniX ... maximum recursion depth exceeded :(

[@know1374]

I'll take $3M to release a different and more powerful ncov strain. You'll never stop plotting, trust me.

[@joshua43214]

@Tucsoncoyote 2019 Yep, got some stats myself. The stats do not lie - the people do.

[@janram987]

This is awesome and one of the best videos I have seen so far!!

[@bArda26]

Great video,your animations keep getting better!

[@vanibandodkar31415]

This is the best channel on KZbin in my opinion.

[@hannescamitz8575]

"It clearly has to decline some day" no Plague Inc player ever said.

[@PeterSedesse]

Everyone to Greenland!!!!

[@hannescamitz8575]

@vadda afffg vxfvd dfvgg fdvff f Guess it does, because of Greenland!

[@xcrazi9461]

@vadda afffg vxfvd dfvgg fdvff f It declines because there isn't enough people alive still xD

[@hannescamitz8575]

@@xcrazi9461 play the gme and you'll understand the jokes. 😉 Cheers.

[@xcrazi9461]

Hannes Camitz I’ve played it, but it’s been a while is there like a newspaper or something?

[@reinerwilhelms-tricarico344]

"If no one is worried, that's when you should worry." Indeed.

[@PrOBOY251]

Everyone is worried.

[@reinerwilhelms-tricarico344]

Party PETE I should have said : if no one is worried you should worry, if everyone is worried suppress your reflex to panic.

[@PrOBOY251]

@@reinerwilhelms-tricarico344 Understood! Yes I agree.

[@andrewharmony]

I hope they do an updated version of this with the new numbers in a month or so. I followed along with this video and did the math for current numbers and we're worse off projection wise than the numbers in this video shows. Especially because based off the numbers in this video, it showed us hitting 10million cases by April 22nd (not including confounding variables), but with the updated numbers as of today we would hit about 22million by April 22nd (not including confounding variables), so more than double.

[@RepentantWall]

Andrew Harmon the biggest issue with being accurate is knowing the actually amount of cases out there. With lack of knowledge, individuals that may be infected but not getting tested because they just ride it out like a cold/flu, and those that are asymptomatic, you start having to looking into statistics instead of straight math.

[@Leyrann]

I suspect that we are currently seeing a correction phase for the limited testing in previous weeks around most of the world. At the same time, I also think we will see and continue to see a lower reported number than the actual number for two reasons. First, some people show limited or even no symptoms, and may not see a doctor, and second, even those who show 'average' but not dangerous symptoms and go see a doctor may not be tested because the doctor decides it is more important to test someone who is more ill and is more likely to require help. The second would be a suspected case (though I believe most governments don't actually keep track of these suspected cases), the first wouldn't be registered in any way (but could still cause other people to be infected if the person doesn't quarantine).

[@SIGSEGV1337]

The news tomorrow: Science KZbinr predicts billions of Coronavirus infections

[@know1374]

You need to see the vid again bro. Certainly not predicting billions of infections.

[@Asdfgfdmn]

Know 1 he was being sarcastic about the media’s strategy of taking things out of context

[@dom9816]

@Tucsoncoyote 2019 that's a game bruv

[@huawafabe]

@@dom9816 that game is praised by scientists and virologists.

[@Danielagostinho21]

You are probably joking but that might really happen somewhere in the world

[@algorithminc.8850]

We love your math channel - one of our favorites. We link to your video here from the epidemiological models section of our company home page. Thank you again.

[@ahmedehsanurrahman4185]

Brilliant Presentation. The best in the category that I have watched.

[@markkennedy9767]

Another brilliant video from Grant. The way he connects intuition to mathematical reality always amazes me

[@sabbiushah4822]

Now, I would like to see a follow up video explaining what actually happened, from data perspective, after everything goes back to normal.

[@zyzxzsgedr]

I second this !!

[@rohanvig8118]

What if he doesnt survive

[@nilstrieb]

@@rohanvig8118 No follow up video then.

[@unitrader403]

as it currently stands in the worst case the follow up video will come from 2blue1brown

[@letsbehonest4221]

Don't hold yt breath. All these vids useing mathmatics to explain a viruses spread rate will avoid such vids like the plague

[@yxu6460]

"If people are sufficiently worried, there's much less to worry about, but if no one is worried, that's when you should worry." So true.

[@dwightk.schrute6743]

One of my upper div physics professors just emailed this to us.

[@timwelch7332]

A lot of good points here. I would like a discussion about the hypothetical calculations regarding networking and the "six degrees of separation" rule and how certain nodes with more links can rapidly increase the effects of exponential growth.

[@alexjones4president]

"It's easier to fool people than it is to convince them that they have been fooled" - Mark Twain

[@isynciswim7382]

not me, I'm both easy to fool and easy to be convinced I've been fooled.

[@reinatr4848]

That is because you dont show us proof you Vitamin D deficient rodeo clown.

[@cfrandom]

Fooled again: www.snopes.com/fact-check/did-mark-twain-say-its-easier-to-fool-people-than-to-convince-them-that-they-have-been-fooled/

[@robin9793]

"We've been tricked, we've been backstabbed and we've been quite possibly, bamboozled"

[@reinatr4848]

321ozzy Yeah, and we call the flu Influenza; what's your point, you negative IQ troll?

[@deleetiusproductions3497]

Been quite a while since you uploaded. Good to see another upload from you.

[@kurtkotknodel7336]

Thank you so much for this video! It reaches so many people! Now that I am already isolated myself quite some time, my roommates threatened to kill me if I lecture them one more time about exponential and logistical growth. But I didn't make any video about it nor do I have the proper range. You are some Educationhero & the world needs people like you!! The amount of bs I heard from people around me in february was astonishing and nearly broke my spirit. Stay safe

[@kayligo]

Kurt Kotknödel stay smart and stay alive. The world needs more smart people

[@kurtkotknodel7336]

@@kayligo I will do my best. My heart goes out to you as well, wherever you might be. I hope you and your loved ones will outlast this crisis. The only thing I can do now is to act smart and to keep good thoughts for everyone out there. We are all in this together!

[@AjaySakarwal]

An example of logistic curve I can see in 3Blue1Brown's videos is the speed of animation. At first it starts slow which then increases rapidly. At the end it dies down. Which is one if the reasons why the animations look so mesmerizing in these videos. Just a thought.