Exponential Growth is a Lie

[@kaiyuwang6755]

Very educational. Thank you! I am an electrical engineer with control background, and your control bootcamp is a good review class for me

[@fhz3062]

As my Prof at the Introduction course to the Ordinary Differential Equations said. "Love and dx/dt = a x wont last forever, on the other hand, some may behave as dx/dt = -a x(x - b)". It took a while to understand such profund thought.

[@nathanielkilmer5022]

These videos are so good I end up watching them when they're not related at all to what I'm supposed to be studying.

[@raghebalghezi9532]

Thank you so much! This is truly edifying.

[@Eigensteve]

You are so welcome!

[@alfonshomac]

you rock my dude. thank you for these efforts. I'm applying for grad school. Hopefully, maybe I get an elbow bump in person at some point in the future.

[@marofe]

Thanks for your commitment to providing high-quality content. However, can you give some references where we can dig deeper into these ideas and equations?

[@LightbornKinoko]

Try this classic by Smale. doi.org/10.1016/C2009-0-61160-0

[@rhi9551]

Tanks for strong presntion . You one of the best professor control in the world.

[@phpn99]

Thank you for a nicely-done video on an important topic. Not enough people know about logistic functions and their relationship to chaotic systems. One thing I'd like to point out, is that in all of the recent discussions that have centred on the dynamics of the Covid pandemic, there's been the strange assumption (in my view) that the infection could spread to the entire population, or to some "herd immunity level", the value of which you'll hear would span between "60% and 90%" of the population. This would entail that the carrying capacity for the virus is nearly infinite within the population (that is, 'herd immunity' is a ratio of the total population, which is then 100% susceptible). But to my knowledge, there are no recorded examples of viral epidemics that have ever spread beyond 20% of the population. Even highly contagious and sub-lethal rotaviruses, never have the chance to spread beyond 10-20% of the population. At its peak during the 1950s before widespread vaccination, smallpox infected 50M people, or 2% of the world population. A cursory inventory of this will reveal that more successful infectious agents, like falciparum (causing malaria), need to be spread by an active parasite, in order to break beyond 20% infections. The peak recorded for malaria was close to 60% in Burkina Faso, at the end of the 20th century. In summary, historical evidence points to a much lower carrying capacity for viral infections, than what seems to be assumed. This, in stark contrast to all that has been voiced in the press and by officials during the present pandemic. I believe it should be possible, by analyzing past epidemics by viral agents of similar contagiousness, to infer the actual population carrying capacity, per virus type. This carrying capacity must be a complex function of environmental factors, as well as biological (host-related) factors. As complex as this system may be, it would naturally boil down to a single capacity metric, expressible within a confidence interval. I would be happy to be proven wrong; just show me the data.

[@evanparshall1323]

For some reason, I calculate the number of bunnies converging at 20 and not 40. This is because x,k+1 = r * x,k * (1 - x,k / X) where if r = 2, X = 40, if x,k = 20 then x,k+1 = 2 * 20 * (1 - 20 / 40) = 20 which means convergence as this would repeat forever. I believe it would converge to 40 if you replace the x,k+1 with dx/dt. www.wolframalpha.com/input/?i=x%27%3D2*x*%281-%28x%2F40%29%29

[@chatterb]

Thank you Prof. Brunton for putting your wonderful lectures on youtube. The way the topics are dealt here makes me think that the coolest research is happening at your lab. A minor comment, I think the first term for dI/dt in the SIR model should be positive. The rate of change of overall population should be zero,

[@G12GilbertProduction]

These video about exponentials whose you recommended, where's got link?

[@Optinix-gz1qg]

amazing channel and great explanation !

[@jithck9832]

i love the way u edit ur videos

[@Peter-zh3bh]

Thanks, Prof. Steve. Very informative.

[@Eigensteve]

Glad you enjoyed it!

[@arcade-fighter]

I would like to remark a mismatching between what you say in minute 4:22 and what you have pointed out on your board. You said: "When your population gets closer to the maximum, this gets closer and closer to one, and your exponential growth gets multiplier by a number which is closer and closer to zero, so slows your exponential growth". The equation x(k+1) = r * x(k) * (1 - x(k) / X) and what you said don't match leading to confusion. Actually, the equation (1 - x(k) / X) should get closer and closer to 1/r to make the population x(k) to stabilize around its maximum capacity (which is not X as you said as well). Actually, the equation on the board is the logistic map, which is a chaotic system for a ranges of r values. I think you are confusing it with the following differential equation dx/dt = r x * ( 1 - x / K). the solution of this is x(t) = K / [ 1 + ( K - x0 ) / x0) * exp(-rt) ] , taking limits x(t) when t -> inf, makes x -> K

[@tedsheridan8725]

I think your equation at around 4:00 is incorrect. The logistic equation is written using the derivative, should be something like x' = rx(1-x/C). If you write it as a state evolution equation as you have it, it doesn't converge to X, and can even be unstable.

[@pablomiller9253]

Great video Series! Keep making videos.!

[@anthonyfrias8864]

Nice videos! You mentioned economy. After Covid, it seems to be the next worry. I wonder if we could look at the economy from a control perspective to understand a bit better the dynamics.

[@danielhoven570]

I remember trying to explain this to my brother who thinks that the world population is going to keep spiking exponentially. In VA they give you 6 deer tags with your hunting license just because the deer's natural predators were all driven out by developers.

[@bobipineman]

Even when removing hunting starvation disease and car crash are good population control

[@JDQJDQJDQ]

i think there's a mismatch of notation. shouldn't the bunny equations be, if in discrete time, x_(k+1) = (1+r)x_k and x_(k+1) = (1+r(1-x_k/X))x_k? or dx/dt = rx and dx/dt = rx(1- x/X)

[@medmamounbay8622]

Thanks for you prof

[@pipertripp]

Steve, why isn't the prey death rate modeled in the Lotka-Volterra model? Is the idea that prey just get eaten as the cause of death otherwise they remain in the population and contribute to the population increase?

[@deepbeginning]

Thanks Professor!

[@hopebelhafsi5630]

this nature it can't have laws and rules to follow in order to solve these kind of problems ...Thank you so much 😁!

[@looper6394]

Doesnt exist? What about Universe Expansion?

[@Eigensteve]

Well... is infrequently unchecked :)

[@randywelt8210]

But all matter is bound to speed of light. So hubble constant might be the only real exp. Growth, but we will prob. never have the chance to fully exploit it.

[@MADSK_LLZ]

The initial inflation tapered off to the current (very very very much slower) rate of expansion.

[@philiprowney]

@@MADSK_LLZ that is still accelerating =]9¬_D

[@jsc3417]

Can you make a video on Weibull? Bath tube curve?

[@4SDerion]

Very interesting, thank you very much for the videos. Greetings from Argentina !

[@pipertripp]

LOL. When I first saw this in my feed I thought it was some conspiracy/flearther video, but your name looked familiar so I closed my eyes and clicked the tile. Glad I did.

[@robmarks6800]

Error in dI/dt: first term should not be negative

[@adinovitarini6173]

Interesting Prof. and thank you for sharing

[@The_Tauri]

Instead of calling it lies, why not just state that there's implicit assumptions that will get challenged once things get big (or small) enough and that in the macro world, there are no pure functions. It not technically a lie.... one could make the same arguments about many kinds growth functions - for example, even for a simple linear growth curve, a naive extrapolation over a long enough time scale will *always* overrun the finite capacity of any finite system like ... the world population. So what matters is that the slope of the growth function eventually tapers off (because of interesting reasons we need to understand) and thus, of course, the higher order derivatives need to be taken into account if we're talking about long time scales.

[@Eigensteve]

Fair enough... the title is mostly a joke. But it is true that there is almost always some saturating process preventing true exponential growth.

[@The_Tauri]

@@Eigensteve Sorry didnt mean to sound all holier than thou... love the content and clear presentation, keep it coming!

[@myscience11]

This is 3rd video I think? Or I missed one?

[@TEC_STE]

Very very usefull and wonerfull .You are the best 🌸🤗

[@talhazeb4021]

Yes I think 3rd video

[@phamhongvinh550]

Interesting and informative!

[@MrGeometres]

The same argument in principle applies to any unbounded growth. Linear growth, even logarithmic growth. Just takes a bit longer.

[@haimbenavraham1502]

Nice to know were related.

[@rhi9551]

Dear professor,please intrduce LPV systems. Tanks

[@georgemissailidis3160]

1:45 sweet home alabama

[@consultanta-aec]

Still, who said that exponential growth would go on forever?

[@Ting3624]

Nice click bait title LOL good video as always

[@adamludwick9931]

Could you kindly forward this lecture to Dr Fauci and others who refuse to add saturation and decay into their models?

[@Eigensteve]

Oh, I'm sure many of them know. But it begs an interesting question... how complex of a model should we try to identify under extreme uncertainty and limited measurement data?

[@The_Tauri]

@@Eigensteve Excellent point - this situations seems to be a great example of how hard it is to do highly consequential decision making with highly uncertain and rapidly evolving data!

[@markusantonious8192]

The notion of 'getting off this planet' is a total pipe dream - certainly within the timescale of the exponential population and environmental pressures facing us - and yet there are no end of technophiles who trot this meme out time and again as though it is some sort of feasible solution to the attendant crises facing us. Indeed, the essence of the technophile response leads inexorably to the ultimate in obsolesence - and obscene - ideology: The Throw-Away Planet.

[@graithtools8215]

Sigmoid growth applies to physical systems so long as choke points on physical growth exist. There are intangible systems lacking such limitations. There's no limit on absurdity, for example. Real bunnies? Limited in a forest. Unicorns? Can grow infinitely. Systems don't have to stick to one forest, however. Even physical systems can expand as bunnies explore to new forests. The limit is then the limit on new forests. And then there's Elon Muskrabbit, who flies a bunch of bunnies off to Mars and creates new forests there, refining interplanetary bunny travel and extraterrestrial forest growth, until the physical limits of the solar system is filled, which is an ill-defined limit potentially so much larger than one forest that exponential growth may as well be considered true. The same happens with COVID-19: while SEIR eventually gives herd immunity and a sigmoid growth curve under a simple set of assumptions, those assumptions appear to be invalid: recovery (therefore removal) appears to be of very short duration, antibodies appear to be of very short term effectiveness (converting R to S infinitely), and chronic health effects just get worse and worse expanding the intensity of I, with a likelihood COVID-19 will be with our species possibly forever, a disabling horror that in no sense ever stops growing in its cost to us.

[@SSNewberry]

There was a "Probability Zero" story many years ago.

[@abhi57655]

Loved it

[@stephendean2896]

I don't mean to disagree and most likely I am wrong. If so I am sure the KZbin comment section will gladly point out how wrong I am Take c² (speed of light in a vacuum) as an example If you had a spacecraft that was trying to reach the cosmic speed limit. Then at some point the amount of energy needed to increase the velocity even a fraction of a second faster would take an infinite amount of energy to do so I guess once infinite is reached then that ends exponential growth

[@mattisbette3932]

Nice video. Have seen so many hilarious calculations where they just put a regression on the data and just assumed it would be a perfect prediction of the future. For those who are interested there is a article about how fast men and women, where running a marathon (it was from ~1980 f i remember correctly) and even tho women have always needed more time their record improved faster then the mens record times. And the article came to the conclusion that women will faster then men one day, but they went with a plain exponential regression of their data so they also predicted that women will run faster then speed of sound one day. Needless to say neither of those event ever happend. The second example had to do with immigration of refugees in europe, where the alt right wanted to give their great replacement theory more weight and so they took the increasing number of refugees and made an exponential model, which supported their theory. The thing is you could see really soon that the model was of because by 2060 there would have migrated more people from africa and the middle east to europe then their are currently living in africa or the middle east.

[@isbestlizard]

Doesn't that imply that bunnies only multiply half as fast, when the population is at half it's maximum? I'd expect they'd keep multiplying RIGHT UP to the point they couldn't any more. They wouldn't slow down just because they 'knew' they were half way to the limit.

[@isbestlizard]

I don't think wolves work that way either.. they don't eat ten times as much just because they're in a territory with ten times as much prey

[@epicmorphism2240]

Yes we are all related, max 50th cousins!

[@kartikeyasaraswat2736]

Very informative... Interesting as well....

[@peaceking211]

What does "Exponential Growth" really refer to? Does it actually refer to something deeply evil an "excuse" to perpetrate it? "Bunny's getting eaten" says so much. Don't forget kuru disease.

[@DinHamburg]

Australian environmentalists surely agree with your population dynamics...

[@BioLogicalNerd]

Click baity title. There's no "lie" but misrepresentation here. In the mathematical field, sure you can have exponential growth. But in fields such as biology everybody knows the expontial growth phase tapers off after a while, so to imply that the "lie" of expontial INFINITE growth is what is being taught, is in itself, a lie.

[@SRIMANTASANTRA]

Hi Professor Steve, Great, Thank you.

[@BarkanUgurlu]

you mean Lie algebra? :p

[@The_Tauri]

lol

[@levisding6724]

VISTING MY COUSIN STEVE!

[@harshadsalunke1580]

So you are my cousin..

[@belalmohammed2265]

Hello my fellow cousins :)

[@Snuni93]

Sorry, but this is a super click-baity video title, which is obviously cashing in on the current media hysteria about a pandemic. Much like how a mathematically pure and infinite exponential growth doesn't exist in the real discrete world, so do lines and circles not exist. Within a certain frame, you're more than justified in identifying natural systems and elements as "circles", "lines", "linear" or even "exponential".

[@tetbundy5683]

Just say the i-word