@@nickreed7277 or he means that it is elementary level algebra, not in relation to schooling, just that he struggles to understand the basics of algebra
Yeah, another well done video. I am left wondering the relevance of the Mandelbrot Set though. I'm not a mathematician, and I've never heard of it before. I'll do a web search, but would have liked to hear about where the equation came from within the video.
That and the "shadow" of a 4-dimensional cube passing through 3 dimensional space are the coolest mathematical animations I've seen. Matt parker shows it at the end of his talk at the Royal Institute if you're interested.
When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained 💜
The video didn’t really explain the behaviour though, it just made an observation/comparison to the mathematics they were talking about. I’d be interested in a more in depth video that actually explains why we see this behaviour so often
@@dmajorvgm8735 Well, noone knows WHY, people just noticed where it matches the algorithm. And why may be, I strongly suspect, some extremely fundamental basis on which the whole reality has existence, hence why this video is quite startling.
Feedback from UCLA A/Prof Heather Zinn Brooks: "At first, it seems totally crazy that increasing r would lead to cycles... if it's describing population growth, why would a bigger r cause a drop in some years? In fact, the magic is in the (1-x_n) factor of the equation, which models a carrying capacity. The idea is that populations are typically resource-limited, so growth can only be supported up to a certain point. Once you think about that, it makes sense that huge growth rates could result in "boom and bust" cycles in the population, because the population would grow faster than their resources would support."
As a control systems engineer, I've seen this behaviour before in several systems when control goes awry. Now that I know there might be something I can do about it, this opens up all sorts of possibilities to new control methods. I'm freaking out a little bit.
Actually the first physical chaos measured was an engineer using a simple circuit with a transistor and a harmonic input, where he sometimes saw one period, sometimes two, and sometimes all of them
Wow, you could control something back from the edge of chaos or even from already started chaotic behavior (like an airplane already entering an aerodynamic stall) using the methods that those scientists used on the rabbit hearts! I hope you're looking into that paper right now lol.
@@brocktechnology I'm super excited for the possibilities of better control algorithms by using something analogous to the research in restabilizing heartbeats, the implications are awesome for aerospace engineering.
Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.
I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.
Good point. But there are people who can actually connect those things naturally. I think this is also a skill on its own - we don't need to be thought because we see those patterns interacting each other and what have presented seems to be trivial...
100% i always thought that we would have leaps and bounds of breakthroughs in understanding the entire structure of the universe if we taught students in school basic math... and then showed them crazy concepts like these in the hopes that one of the billions of people on the earth will see them and go "huh that reminds me of x, what if we apply it here?" rather than pushing them through advanced mathematics to get degrees not only that but if you look up slow motion explosions on youtube and look closely the inital explosion looks like the mandelbrot set, and you can see that as it expands there are little bits of contraction in every single explosion if you take it frame by frame i watched this video when it came out 3 years ago and i've been obsessed with the concept ever since
A lot of this video is centered in something you might find in a numerical analysis class. I just took one in college and we went over a lot of this kinda stuff.
Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !
But this formula can't be applied to many things! Bacteria and humans are good example of that! Rabbits are not a good example as they simply die a lot... You don't even need some madeup formula to explain the populations interaction in biology. More rabbits mean more food for eagles ;). Lets say the formula normally works. Well if you reduce the death rate of rabbits by placing them on another (safer from humans and eagles) planet the formula wouldn't work for a very long time...Also sudden increase in rabbits population would mean that they don't have food and die from starvation but again this is preventable and generally there are tons of changing factors involved.
Feigenbaum constant: Works for all recurrences that come from functions with a single hump. A mathematician: Well, we have to demonstrate that A computer scientist: Give me the Summit supercomputer for a few days to find a counterexample
Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!
You're heart chaotically fibrillated, you maybe dying haha. Nah that's mad though. If you're heart did actually double beat, that was literally an example of the video. So strange, and even stranger that complex numbers that exist on a plane we can't see are linked to all our hearts and the rest. One day we'll understand maybe. hah
"How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!
This is getting out of hand, now there’s two of them... wait four of them. Hold up. Eight of them... wtf a chaotic number set of them??!? This really is getting out of hand. Oh wait no just two of them.
Having just watched your video on the ubiquity of 37, I couldn't help but notice that was the first example you provided when taking about period doubling sequences of any length!
If you observe a subject watching this video at a specific fraction of the speed of light, you could see it at 18 minutes no matter what the subject's playback speed was.
@@mikeciul8599 It is the real part of the complex value returned from the complex logistic map. If the result was also complex the Mandelbrot set would be 4D.
@@NightBeyondVeil We can't imagine that. That's like asking someone to imagine a one dimensional point. Yes, some cosmologists want to say that was what the singularity was at the beginning of the universe, but think about it, it doesn't make sense.
So, basically, 'Chaos' is a misnomer now. There is clear method and math to the madness. Are we really living in a simulation :-)? Sometimes, it fascinates me to see all the advancements made in math, science. probability. stats etc with a simple thesis to put some structure/framework to quantify the world around us. It has helped us explain a few phenomenons, create products, even predict stock prices, human behavior (looking at patterns and trends etc) but the other part of me is conflicted - for life and its energies cant be modeled. It's too fascinating to be modeled out and the vastness of the universe and my spiritual beliefs are a complete anti-thesis to my scientific side. Heck, even science is ever changing - now, we are discovering qubits - particles that carry both -ve and +ve charges, which has deep implication to our view of physics and the world around us! While amazing, how much can humans really 'figure out' vs realizing there is something more to life that what even our more prolific attempts at math/AI/ML will ever get us to.. Or, perhaps, there isnt a higher power :-)?
This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!
@@GdeJ I am from Politecnico of Turin in Italy and we had the pleasure of having a lecture directly from Professor Chua. I think the Lorenz Attractor and the Chua Circuit are the most thought in control engineering degrees. Maybe talking about non linear systems behaviors we also have systems having limit cycles in the phase portrait, for example the Van Der Pol Oscillator
@@albertofoti4152 I'm from Federico II University! I just had an exam on non linear dynamics and control. Other than Van Der Pol oscillator, our professor mentioned also other relaxation-excitation oscillators, such as Fitzhugh-Nagumo and Hindmarsh-Rose models of a neuron.
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
@chcpr1 i think its more that no one in power cares to invest in school systems to make them better, but I dont think they are shitty on purpose, just due to neglect. Why would rich government officials care about public schools when are their kids are privately educated anyways, you know?
Unfortunately, this simply isn't true. I'm a high school math teacher, and I've shown this kind of thing to my students on numerous occasions, and the response is pretty much always the same; disinterest. If it's not on a test, they see it as an excuse to take a nap, zone out, or work on other classes' assignments.
Something tells me that you might have said the smartest thing in these comments. Music is vibration, vibration is periodic. This equation probably can be found in music somewhere...
This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.
I feel so dumb! I have a PhD in Ecological Modelling, I have used this equation - and more complex version of it - to model population dynamic multiple time and I didn't knew of this Feigenbaum constant!!! I had teaching on Chaos and none of my professor mentioned it! Well, thanks Veritasium for teaching us new things!
Bruh I'm just an eight grader. Tomorrow's my maths test and I'm supposed to learn mensuration and algebra but I'm here trying to figure out what this video even is about after watching it for the 7th time.
"The mandelbrot set is numbers that don't blow up" Mind blows up. Seriously the best explanation ever. Then he shows it in 3d. Learned more in 20 minutes than in the last 20 years.
.Turn to United Brethren Church. Using the Lords name in vain is a sin and so is cursing upon your enemies. And so is saying anything hateful, premarital sex and lust are all sins..⁰
You really did a good job with this one. This is something that’s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didn’t believe me! This stuff seems so fundamental, but it doesn’t seem like it’s tot as a unifying principle when it could be. It’s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.
I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately 😃❤️💕
That's probably the ideal situation. If a tutor were to customize a lesson for you specifically, they'd probably aim for a difficulty level you'd find interesting, and a lecture that you could mostly follow. You'd also be very slightly outside your comfort zone, to give you room to "grow into" the lesson. It would also be a bit challenging and would leave you with a few questions to mull over, thereby slightly increasing the chance of watching another video, or of reading a book or article on a similar topic. Your comment would probably be music to the ears of a lot of educators.
TH-cam algorithm - 1st stage - sends to people who are actually interested in math. Less views 2nd stage - sends to related viewers. Less views but still constant. 3 stage - Sends to random people on their feed. Fluctuations in view cycle (no negative views so it shoots up) 4 stage (chaos) - recommends to people like me of all people. Millions of views
My apologies! if you are not interested in my offer I am from Russia .I live in Siberia looking for a sponsor (investor), please send this information to interested parties and companies..Thank you for reading with respect Popov Gennady. Today, for all progressive, caring people who care about the fate of the planet, the fate of people, the fate of humanity! Today, it is unequivocally and irrevocably clear that warming is the main threat to humanity. It is extremely important to pay attention to projects that can change the situation on a global scale. to stop further warming. The main supplier of gases that provoke warming is a thermal power plant, which burns coal, gas, oil,...and the atom, too!. Exactly my invention… Still I ask all people who are not indifferent to the problem! convey this message to interested parties and companies...
This is like when you start a new project or new year resolution. Everything is fine and simple at first, then progressively and unexpectedly everything turn to chaos
I ran across this video about a month into my discrete dynamical systems course. It has been super helpful to have something that gave me some intuition surrounding these patterns before I encountered them formally in class. Sharing it with my professor now :)
I saw the video title and thought “oh suuuuure this will change my life”, but wow I did not expect to be so taken aback by this. Something so fundamental which I’ve never heard about before!
I watch this every single time I think about this concept. To be honest, one of the best decisions ever to beat this into my head. thank you for making this.
14:00 I played with this when I was younger and was fascinated to hear the different rhythms it makes. And here I am a decade later learning about it on youtube.
Do it 👍 Maths is the supreme language of the universe. If you wanna understand the universe, math is the way. I embark on the same path and it's amazing
Manamrit Singh not really, mathematics is an abstract concept and it won’t make you understand the universe. It is more of a tool that you can use to „understand” the universe through physics. I know several brilliant mathematicians who decided to study physics when they understood the difference. Mathematics is not really that interesting when it comes to studying it. It’s the same as learning about black holes in physics, it’s a very brief lecture compared to other stuff that might seem boring like mechanics, kinematics, rigid bodies, aerodynamics etc.
I taught myself basic calculus from videos on TH-cam. Both Khan Acad and 3blue1brown really helped. I was able to skip Math 251 (Calc 1) at my college and move straight to Calc 2 after a 4-year break between studying BASIC algebra in high school and returning to college.
@gamecube.enthusiast - - i did, but the fundamentals were studied in years 5-9, then it was trigonometry and calculus. Actually, i just realised it depends on what you call 'highschool'
I've been studying emergent behavior since the 80's, when I first read Conway's Game of Life. Back then, it was treated as a nuisance, irrelevant, and annoying. I love watching the break into oscillation as your R-value changes .That's the same behavior as a damped spring, or feedback in an audio system. The transition to chaos between states makes a lot of sense. I love the visualization of the Mandelbrot set, that gave me the perfect starting point to understand it in another dimension. Wonderful.
lol, I can tell it's true, chaotic equations do exists, however it's funny how the father of chaos theory wasn't even a mathematician, he was a meteorologist.
That is the scary part of learning on TH-cam. Thankfully he provides a lot of references :) I avoid taking information from TH-camrs as facts unless they can back it up
You may have broken my amount of mind-blows in one video - the z-axis of the Mandelbrot set? The chaos of Bifurcation? The bifurcation constant? The practical applications? Incredible!!
One thing he didn't mention...there's a second Feigenbaum constant. Not just the length of the tine with its subtine 4.669, but the width of the subtine 2.502
that 3D fractal diagram of the mandelbrot set expanded into its bifurcation expressing form in space, I've seen it before this video, and almost comprehended its nature, but now i see it clearly. and it's so beautiful. that is the single most beautiful object that mathematics has given us.
Ah, so you really have been paying attention! That seems to be one of the more important lessons to learn in life. So, here’s to you, me, and everyone else realizing we know less and less each year! 😀
Feels like when you are using exponential equations your inputs are very important and deserve a lot of explaining why you chose it, regardless of real value or best estimate value
I used to notice my sink doing this when I was a small child and always wondered what the heck was going on. This video just solved a 15 year old mystery for me. Thank you!
I did not even realise how quickly 18mins passed by. Love you vertasium I want to grow up and do research and share on TH-cam just like you . You and Physics Girl are my favourite youtubers
If you're not aware of PBS Space Time, give them a watch, too. If that's too heavy, check out Isaac Arthur. If you're more into physical experiments, Applied Science or Practical Engineering are great channels. Of course, Numberphile, Sixty Symbols, Periodic Videos, and the rest of Brady Haran's channels are all good, too.
Nice choices my friend! Hopefully you already know the channels Smartereveryday and SteveMould. If you like Derek then you'll enjoy these guys too I hope.
When i had numerical maths in my University, there was a alot of chaotic stuff we came along and philosophised with our Professor about. Was one of the best classes I ever had
Math professors are a lot more mystical than people give them credit for. When I took Calc II in college, I went to my prof and talked about the weirdness of infinity. I don't remember exactly what I said, but he got the funniest look in his eyes and said something like" in many ways, that is the great mystery behind all reality." Then I realized that if you spend your whole life studying math, it must really change your perspective on everything. Peering down into an endless sea of perfectly tuned complexity that most people never think about, and wondering why it's there or where it comes from...sheesh.
Your videos never failed to make me think about what is the purpose of this universe.. why is it there and how it works so perfectly without anyone controlling it..
You’ve re-kindled the magic! I read “Chaos” thirty years ago. It changed the way I see the world / time / history / physics. Please keep following this path ... you are blowing my 63 y.o. Mind! Thank you!
I wish math was taught this way when I was a kid. We did a lot of one thing at a time (sausage stuffing, as we call it in Sweden :), but never got the explanations of their relations and that you can express something in many different ways with graphs, trigonometry etc. Granted, I chose the humanities side of studies later on; but if my teacher showed that an equation can be found within the Mandelbrot set or how you can represent it in many different ways, I think it would have created a lot more interest. This was a couple of decades ago, but still I wish my teachers had just scratched the surface of what lies beneath the "repeat this type of equation until your eyes bleed". Time to go out and shout at kids about how things were better yesteryear and that we only had tape recorders to store data on and 8-bit consoles. And, of course, that we walked 8 km either way to school, uphill in both directions with snow all year 'round.
You're also expecting the teachers to understand this subject and teach it. Unfortunately most teachers just regurgitate what's in the "teachers manual"
@@deman817 I have a couple of friends who are teachers, and the level of education they have to reach to be "certified" is way above what they teach. I guess it's a question of enjoying your work. You are definitly on to something though; the difference between an Office space-type and Dead poets society teacher is quite broad :) Also, at least locally, the work of education is relatively low paying. I'm probably naive in thinking it should be a kind of important thing no matter if the school is private or public. Money, money, money. But now it's time to go out and tell the kids of today how we used to play with twigs and cones; and we had so much fun! They don't know how good they have it today... *mumbles about the price of milk*
The real truth that they don't tell you is that 99% of math in school is building up to one thing ... and that is Calculus. It's this that is important above all and gives you 99.9% of the things you have in the world. That's the main connection/secret that is missing.
I swear to god, my mind was blown away by that! I had only ever seen the Mandelbrot Set as that 2 dimensional boundary thing, so seeing that it was actually a 3D-thing was insane
After watching this video I realized that math wasn't the subject I didn't like or found interesting. Math teacher was the subject I didn't like or found interesting.
Same, when I began they wanted to hold me back a whole year, yet when I was in 8th grade they refused to let me go to Highschool since I had finished all their math classes, so I had to take the same class over again. And they wonder why kids start smoking pot... I learned I hate the school system. They also had this space program for the gifted, and of course I was not invited in the beginning even though I was interested, they invited my only friend, and I asked, but they almost laughed at me. A couple years later in 5th grade they asked me if I would join, gave me a tour that was terribly underwhelming, so I explained and declined. Then in Highschool AP math the teacher yelled at me for asking a question he proclaimed was a stupid question in front of the whole class and refused to answer it even though he preached there are no stupid questions, totally making a fool of me. I dropped out and went to art Highschool, which was amazing. I went to community college for academics and even got college credit knocking off two credits for one course. Later the school begged me to come back because I took their tennis team to state as a freshman, but I couldn’t deal with their BS anymore. The best teacher I had for academics was a drunk history teacher, loved him, was passionate and I actually learned because he cared about history. I hear schools have only gotten worse in the last 25 years, but good thing we have such a massive military that you hardly need a Highschool education for. We really need to pay our teachers more!
Not really. All these are based on more elementary mathematics you learnt in school (from elementary all the way to university) that requires "repetitive and boring" work. You can't dive into this interesting topic without a solid foundation, and the way to be good at everything is the same: you have to do it repetitively (though great intelligence is also crucial for a subject such as Mathematics). If you can understand all the theorems/methods/formulas on the first look and can remember them without repetitive practices, then you are a genius and you should absolutely choose a more suitable path for you. Yet I doubt many people have that capability.
@@evdm7482 I guess your anecdote deserves a counter anecdote. It was joining the military (to get money to go to college) and the military forcing me to learn logarithms and trig in order to calculate great circle distances (by hand no calculator just log and trig charts) and azimuths for HF radio operations that showed to me that math was fun, interesting, and useful. It led me to not only a career in the military (enlisted, not officer) but also to pursue a degree in math upon my military retirement. I am now a high school math teacher. I had great teachers in high school, I went to a great school. I just wasn't interested in academics at that time in my life. It was the military that taught me to learn and to succeed at academics and other things in life. What I really needed was someone in my face, yelling at me, to challenge me. All I got in high school was platitudes and the usual "touch feely" BS that most teachers give to students. I had too many female teachers who really couldn't relate to the inner warrior of (many) male students. I think a few good male teachers could have made the difference for me, but I only had (mostly) female teachers. Now that I'm a teacher I know that my teachers weren't bad (at instruction), just incapable of reaching all students. I'm sure I'm guilty of this as well, I'm never going to reach all students. This is the one of the many drawbacks to collective education. I offer this counter anecdote not as a critique of your comment but to show (in anecdotal form) that it was the military that made me a math teacher and that it was high school level math that I used in the military that has guided my journey.
I love that you mentioned that things like this should be taught to students. I completely agree!! Topics like this are why I started to be so interested in mathematics.
Yes! Math was so very dry in school- as if it was intentionally designed to be so. This presentation would have made math so more interesting had it been included in the curriculum.
So much intelligence, so much creativity and all that comes crashing down when we get to religion Billions follow Master/Slave religions - "we must get down on our knees, swear loyalty & obedience to the Master & only to this master, he will be pleased & keep us in comfort(heaven)" Simple, primitive ideas from simple primitive people being blindly followed by even the best of minds
Dude I have absolutely no idea of anything I just heard but I still listened all the way through it takes a very talented type of person to intrigue his audience that much.
I love how this converges to the VALUE of the Mandlebrot set at each point. I've often seen the drawing of where the set has valid values, but never thought about the values it holds in those areas.
I believe that in those videos of the Mandelbrot set where they zoom in for a long time, all the wild and crazy colors come from the value of the point as well. So visualizing the values in 3D space produces the logistic map with all sorts of chaotic lines, but visualizing the values with color produces a bunch of chaotic color patterns!
"How did I get to be 37 years old without hearing about the Feigenbaum constant?" That is an extremely optimistic outlook on what 37-year-olds should be concerned about.
All praise The Almighty Algorithm! It's the most omnipresent entity! It hears all. It sees all! and It recommends on your behalf. 001100 010010 011110 100001 101101 110011
If you're looking for a good introductory text on the topic I'd highly recommend Exploring Chaos by Nina Hall and if you know what a Jacobian is and want to really get jiggy wit it then I'd suggest Strogatz.
I remember watching this video when I was about 14 years old and being fascinated by this, but my understanding kinda dropped off when the Mandelbrot Set came into the video (I knew nothing about it). Rewatching this video at age 16, I can really appreciate it so much more, now that I understand it. Thank you for introducing me to the Logistic Map!
I'm an electrical engineer in my master studies and had all this Mandelbrot in my third semester and I was so fascinated by it and you brought back the whole feeling of the universe being so mysterious and so logical but far over our understanding. Even in a century we may find new constants or similarities and still can not explain why. The best thing in science is not to understand the physics of the world or to use them but the exploration of things you do not understand, it's like seeing the best magic trick in the world. (and the universe is not gonna tell us how they cheated ;) )
Me: struggles with elementary algebra
Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram
Me: go on
Damn dude. your elementary had algebra? i didnt get to that till highschool
@@nickreed7277 or he means that it is elementary level algebra, not in relation to schooling, just that he struggles to understand the basics of algebra
Bro I dont even know what algebra means
Lol I got algebra in 8th grade in Middle school
But my class was the only one, everyone else had pre-Algebra
Verisatrium :)
I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!
i want this guy on my team after a nuclear holocaust. me and a bunch of mathematicians.
Yeah, another well done video. I am left wondering the relevance of the Mandelbrot Set though. I'm not a mathematician, and I've never heard of it before. I'll do a web search, but would have liked to hear about where the equation came from within the video.
I think you meant: "I am 'A' mathematician"
@@Polarwhisper6 he didnt claim to be an english major
@@christianmathison5892 to be fair there could be girls among those mathematicians.
The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen
looks like a deformed pringle
That and the "shadow" of a 4-dimensional cube passing through 3 dimensional space are the coolest mathematical animations I've seen. Matt parker shows it at the end of his talk at the Royal Institute if you're interested.
But... Humans can't see in 3D... So... Have you really seen it?
@@erteple2647 there is infinite?
th-cam.com/video/9U0XVdvQwAI/w-d-xo.html
This is essentially just a bunch of 3D fractals.
When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained 💜
i've had a similar experience, now explained 30 years later......strange world we live in, everything makes sense, eventually
The video didn’t really explain the behaviour though, it just made an observation/comparison to the mathematics they were talking about. I’d be interested in a more in depth video that actually explains why we see this behaviour so often
@@dmajorvgm8735 Well, noone knows WHY, people just noticed where it matches the algorithm.
And why may be, I strongly suspect, some extremely fundamental basis on which the whole reality has existence, hence why this video is quite startling.
bro you got a new twin
Feedback from UCLA A/Prof Heather Zinn Brooks:
"At first, it seems totally crazy that increasing r would lead to cycles... if it's describing population growth, why would a bigger r cause a drop in some years? In fact, the magic is in the (1-x_n) factor of the equation, which models a carrying capacity. The idea is that populations are typically resource-limited, so growth can only be supported up to a certain point. Once you think about that, it makes sense that huge growth rates could result in "boom and bust" cycles in the population, because the population would grow faster than their resources would support."
1:30 @m in 🇮🇳
I imagine increasing rabbits also increases wolves, so that probably factors in as well.
Yes
This topic came up when I was studying applied mathematics around 1980: en.wikipedia.org/wiki/Lotka-Volterra_equations
Can this be applied to the expanding universe? because it has a growth rate and if I remember right scientists think that that rate has changed?
As a control systems engineer, I've seen this behaviour before in several systems when control goes awry.
Now that I know there might be something I can do about it, this opens up all sorts of possibilities to new control methods. I'm freaking out a little bit.
Actually the first physical chaos measured was an engineer using a simple circuit with a transistor and a harmonic input, where he sometimes saw one period, sometimes two, and sometimes all of them
I was thinking about controls too for most of the video!
Wow, you could control something back from the edge of chaos or even from already started chaotic behavior (like an airplane already entering an aerodynamic stall) using the methods that those scientists used on the rabbit hearts! I hope you're looking into that paper right now lol.
I'm no engineer, but I'm right there with you. I was hit by the realization that this little bit of math is the reason PID is so difficult to do well.
@@brocktechnology I'm super excited for the possibilities of better control algorithms by using something analogous to the research in restabilizing heartbeats, the implications are awesome for aerospace engineering.
Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.
yeah i made it 8 minutes in --with so much struggle-- and then blew up
this is such an underrated joke
up
Pretty much 😂😂😂
Go back
I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.
Good point. But there are people who can actually connect those things naturally. I think this is also a skill on its own - we don't need to be thought because we see those patterns interacting each other and what have presented seems to be trivial...
100% i always thought that we would have leaps and bounds of breakthroughs in understanding the entire structure of the universe if we taught students in school basic math... and then showed them crazy concepts like these in the hopes that one of the billions of people on the earth will see them and go "huh that reminds me of x, what if we apply it here?" rather than pushing them through advanced mathematics to get degrees
not only that but if you look up slow motion explosions on youtube and look closely the inital explosion looks like the mandelbrot set, and you can see that as it expands there are little bits of contraction in every single explosion if you take it frame by frame
i watched this video when it came out 3 years ago and i've been obsessed with the concept ever since
@@mikeinjapan2004You probably notice all of the 25+ functions within plasma/flame 😮😂
Guess you never did psychedelics while in school then😂😂😂
A lot of this video is centered in something you might find in a numerical analysis class. I just took one in college and we went over a lot of this kinda stuff.
Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !
@@shyamkarthikeya4769 That was my point ... :)
@@warrenchinn4114 again a smart man..
Warren Chinn true
@@shyamkarthikeya4769 delete this
But this formula can't be applied to many things! Bacteria and humans are good example of that! Rabbits are not a good example as they simply die a lot... You don't even need some madeup formula to explain the populations interaction in biology. More rabbits mean more food for eagles ;). Lets say the formula normally works. Well if you reduce the death rate of rabbits by placing them on another (safer from humans and eagles) planet the formula wouldn't work for a very long time...Also sudden increase in rabbits population would mean that they don't have food and die from starvation but again this is preventable and generally there are tons of changing factors involved.
Numberphile: Makes video about the Feigenbaum constant
Veritasium: Makes video about the Feigenbaum constant but includes the z-axis
it was a bifurcation
@@unathimatu lol, perfect response dude!
and then there's 3blue1brown telling you what PI has to do with all of this
Feigenbaum constant: Works for all recurrences that come from functions with a single hump.
A mathematician: Well, we have to demonstrate that
A computer scientist: Give me the Summit supercomputer for a few days to find a counterexample
_mind blow_
6:40 When the animation showed the Mandelbrot set being related to the bifurcation diagram my mind was blown...
edstervedster I WANT THAT MODEL AS A CHANDELIER. SO. BAD.
Same here. I am fascinated by fractals and never knew this relationship
@@elee9056 you should make that idea a reality! I'd buy two
The same happened to me! not sure if really they're related... must rewind and check it again.
Crowdsourceeee
Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!
You a rabbit by any chance
You're heart chaotically fibrillated, you maybe dying haha. Nah that's mad though. If you're heart did actually double beat, that was literally an example of the video. So strange, and even stranger that complex numbers that exist on a plane we can't see are linked to all our hearts and the rest. One day we'll understand maybe. hah
When you turned the Mandelbrot on it’s side to show the bifurcation, I’ll be honest, it blew my mind.
That one made me stand up an pace frantically for awhile....mind blown..
@@jingalls9142 same..... It blew my mind.
yeah that was awesome
Same here. Had to stop it and sit back in my chair. Perhaps this is well known, but this is the first time I have ever heard of it.
Its now my wallpaper!!! That image its insane
"How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!
It lowered it for an 18 year old too =P maybe there are even younger people watching, and if there aren't we could share the video to them
@@SergioEduP 17, beat that
InCrIpTiOn 16.
@@arvintis2293 I think krish beat both of us
@Krish Kalra yet here I am during meiozis I
"Oh cool, the Mandelbrot-Set. I have seen that before."
*turns Mandelbrot-Set in 3D*
"What the ...?! That's illegal!"
haha same
I know, right
relatable
This is getting out of hand, now there’s two of them... wait four of them. Hold up. Eight of them... wtf a chaotic number set of them??!? This really is getting out of hand. Oh wait no just two of them.
mandelbulbs are gunna blow you away bro
Having just watched your video on the ubiquity of 37, I couldn't help but notice that was the first example you provided when taking about period doubling sequences of any length!
THat was definitely one of the shortest 18 minute video I have ever watched on youtube. Very fascinating
Now that is a compliment.
this is frighteningly true... I watch it at 1x while my wife brushed her teeth... how's that possible?
wtf, I did not realise that was 18 minutes, I was totally enthralled
If you observe a subject watching this video at a specific fraction of the speed of light, you could see it at 18 minutes no matter what the subject's playback speed was.
I felt Exactly the same. Only by reading your comment I realised "wait... That was almost 20 minutes?"
8:43 - Boom. Mind blown. We've been missing the 3rd dimension of the Mandelbrot set this whole time.
Actually, I think there might be a 4th dimension, because for some complex values of c, the equation could converge to complex numbers.
now imagine the 4th dimension.
@@NightBeyondVeil - no. The world will explode.
@@mikeciul8599 It is the real part of the complex value returned from the complex logistic map. If the result was also complex the Mandelbrot set would be 4D.
@@NightBeyondVeil We can't imagine that. That's like asking someone to imagine a one dimensional point. Yes, some cosmologists want to say that was what the singularity was at the beginning of the universe, but think about it, it doesn't make sense.
Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.
when he rotated the Mandelbrotset on the z axis, i felt that
😂😂😂😂
I did the "Keanu whoa" follow by a long "Duuuude!"
I was like "hol up-"
Hahahahaha
For anyone wanting to study the math of this, I recommend Steven Strogatz - Nonlinear Dynamics and Chaos. That was the textbook I used in undergrad.
So, basically, 'Chaos' is a misnomer now. There is clear method and math to the madness. Are we really living in a simulation :-)? Sometimes, it fascinates me to see all the advancements made in math, science. probability. stats etc with a simple thesis to put some structure/framework to quantify the world around us. It has helped us explain a few phenomenons, create products, even predict stock prices, human behavior (looking at patterns and trends etc) but the other part of me is conflicted - for life and its energies cant be modeled. It's too fascinating to be modeled out and the vastness of the universe and my spiritual beliefs are a complete anti-thesis to my scientific side. Heck, even science is ever changing - now, we are discovering qubits - particles that carry both -ve and +ve charges, which has deep implication to our view of physics and the world around us!
While amazing, how much can humans really 'figure out' vs realizing there is something more to life that what even our more prolific attempts at math/AI/ML will ever get us to.. Or, perhaps, there isnt a higher power :-)?
@@simrans3675 What if it comes that even religion also has mathematics?
@@DHRUVSHINDE-tw5uy Religion is man made, faith/spirituality is a different conversation and tough to crack using math or so I think :-)
Your 3 dimensional animation of the rotating Mandelbrot Set graph conveys so very much information and complexity. Amazing!
YES! Thank you for such well-constructed visualisations. They really are like compact little gold mines of information. :)
I’m an artist and took screenshots of the set graph and logical equation as inspiration. Data really is beautiful.
OMG i took screenshots as well :)
Agreed--data IS lovely.@@3orM00Rrecharacters
people out there proving existance of god with Mandelbrot fractal
its so pretty my inspiration too
This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!
ie: the Lorenz Attractor.
Yep, I'm here because I'm studying for an exam ahah
Non-linear Control and Aerospace applications
Here's another: Chua's circuit
@@GdeJ I am from Politecnico of Turin in Italy and we had the pleasure of having a lecture directly from Professor Chua.
I think the Lorenz Attractor and the Chua Circuit are the most thought in control engineering degrees. Maybe talking about non linear systems behaviors we also have systems having limit cycles in the phase portrait, for example the Van Der Pol Oscillator
@@albertofoti4152 I'm from Federico II University! I just had an exam on non linear dynamics and control. Other than Van Der Pol oscillator, our professor mentioned also other relaxation-excitation oscillators, such as Fitzhugh-Nagumo and Hindmarsh-Rose models of a neuron.
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
@chcpr1 i think its more that no one in power cares to invest in school systems to make them better, but I dont think they are shitty on purpose, just due to neglect. Why would rich government officials care about public schools when are their kids are privately educated anyways, you know?
Yeah sadly they don’t teach you anything your not tested for. Unless they a good teacher.
One of my teachers actually showed us the mandelbrot set and told us about chaos teory. :D
Um, they do teach this.
Unfortunately, this simply isn't true. I'm a high school math teacher, and I've shown this kind of thing to my students on numerous occasions, and the response is pretty much always the same; disinterest. If it's not on a test, they see it as an excuse to take a nap, zone out, or work on other classes' assignments.
When you tilted the graph it made My spine chill , amazing 👏
Everyone here were gangsta till he turned the Mandelbrot-set 3D
Explain?
Please.
@@cfneal1459 r/woosh
@@doctorquantum3364 you can't woosh someone for wanting an explanation.. 🙄
Hahaha
I'm dead 😂😂😂😂
13:57 "What _really_ *IS* a faucet?" - Vsauce music starts
ok John Smith
I miss him
But his video would actually *start* liake that
And finish by talking about *UNIVERSALITY*
"This is water dripping from a faucet.
OR is it?!"
I read the first 3 words of your comment in michael's voice before acknowledging the word "vsauce" in it
So basically like when the bass drops, the tempo keeps doubling until it just goes into complete madness.
The 101 of Speedcore and Splittercore 😂
Something tells me that you might have said the smartest thing in these comments. Music is vibration, vibration is periodic. This equation probably can be found in music somewhere...
I hope a nerdy DJ builds his set this way
I almost spit my coffee. Well done.
@@StormEngineer Imma go brew some coffee so I can almost spit it!
Currently writing a report on chaotic behaviours and bifurcations, remembered this video existed and im so grateful now
This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.
github link please?
I got obsessed too it’s mesmerising
please let us know. I for one for sure want to see it.
the beauty come when u keep zooming it
Oh my, my heart is beating faster now, so, where can I see this art?
Things like these actually make our world more magical than any science fiction
We're living in a simulation and the 4.669 number just happened to be one of the global variable definitions.
@@glowerworm Dear matrix guys don't use global variables it's bad practice
@@eepydragonloaf lmao, maybe it's destiny that every programmer, no matter how powerful, will write bad code.
@@glowerworm so true ... ;)
@@glowerworm Shoulda been 4.2069 imo
I feel so dumb! I have a PhD in Ecological Modelling, I have used this equation - and more complex version of it - to model population dynamic multiple time and I didn't knew of this Feigenbaum constant!!! I had teaching on Chaos and none of my professor mentioned it! Well, thanks Veritasium for teaching us new things!
P. V. I read that as “Executive Meddling”.
@@KarasuInaiga 🤣
@@KarasuInaiga 🤣🤣🤣
Huh
Bruh I'm just an eight grader. Tomorrow's my maths test and I'm supposed to learn mensuration and algebra but I'm here trying to figure out what this video even is about after watching it for the 7th time.
Who's here in 2024 after the 37 video and noticed he said 37 as a random example 😅
Oh yeah, at 6:12
@@Mr_Noob-jp8nv you got 37 likes rn
Pissing me off
He also says he's 37 years old
At 17:02
First time on the synchronicity ride? 😂This 🎢 will only get wilder with time.
Out of all of the TH-cam channels that I don't understand, this one is my favorite.
ROTFL - Nice work Brad! :-)
Lol
LOL ! I'm with you on that.
@@Streamwalker1000 LOL me too
I'm sure you understand more than you thought, otherwise you wouldn't be drawn in. It's about patterns and randomness and how the two shall not meet.
6:37 One of the best plot twist I've seen in my entire life
Hereizer Oh that pun is wonderful
You need to be higher. Great pun
Such a legendary comment, bravo...bravo!
Dad joke levels are through the roof
Get out lmao
"The mandelbrot set is numbers that don't blow up"
Mind blows up.
Seriously the best explanation ever. Then he shows it in 3d. Learned more in 20 minutes than in the last 20 years.
I felt that.
so your saying your mind doesnt belong to the mandelbrot set?
Now that's funny.
@@hannesthurnherr7478 Well, rules are rules, so apparently you are right!
Thank you for making some fundamental mysteries of math/nature at least approachable if not fully understandable to the general public. Great job!
"I'm so excited about chaos" -man one month into 2020
Lmao😂😂😂
@@maumau9466
What that means
@@norpriest521 it means laughing my ..... Off and no im not gonna fill in the blanks
Well, it just tells us someone is messing with the parameters big time.
When things are chaotic, you focus on chaos. And when you focus long and hard enough, even chaos can make sense.
6:41 - "The Plot Twist" figuratively and literally
Noice
pure gold
This whole video is a plot twist
bravo
HOLY
thanks for showing me that as a child i had absolutely no chance of predicting when a water drop will drop.
"when a water will drop" a SINGLE water
😂😂
@@K3zz21 When the water would drop?
Chaos theory?
.Turn to United Brethren Church. Using the Lords name in vain is a sin and so is cursing upon your enemies. And so is saying anything hateful, premarital sex and lust are all sins..⁰
You really did a good job with this one. This is something that’s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didn’t believe me! This stuff seems so fundamental, but it doesn’t seem like it’s tot as a unifying principle when it could be. It’s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.
- What is the answer to the Ultimate Question of Life, the Universe, and Everything?
- 4.669
Nice
It's 42......of course we really don't know what the question is.....(ps. it is 6x9.....which is why it's all fuk dup)....thanks Douglas
Nice reference
It's 3 Pi /2
@@Binyamin.Tsadik 1.5xπ
*_rotates the Mandelbrot plot_*
Everyone: "wait what's he doing"
Me: "he's beginning to believe"
hahahahaha
is it normal this video gave me goosebumps ?
@@futurefacts6909 yes
yeah, you are special...
@@jvm53 she is
You know the video is good when it’s 18:39 minutes long and you still didn’t want it to end
I didn't even notice until you pointed it out, thought it was like 9 minutes
@@Darth_Pro_x I was going to say 9 too. Damn witchcraft.
@@MartinBuzon Next thing you know Derek comes here and tells us that this equation can explain that as well and it was all planned from the start XDD
@@Darth_Pro_x same
It felt like 4,669 minutes
I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately 😃❤️💕
6:43 most underrated placement of the term ‚plot twist‘
Pun of the day!!!!
I love you, man!
german?
Top 10 anime betrayals
i don't get it, please explain !
**slightly opens kitchen faucet*
Me: I'm somewhat of a scientist myself
lmao
Have you written a scientific paper?
Tree Wizard wat
Your comment fits your profile picture so well 😂
*slightly opens kitchen faucet
*
Me in a Joker voice: "I'm an agent of chaos."
I am intelligent enough to find this interesting but not quite smart enough to fully understand... Great video!
covid-19=
this is control over the rabbit population
Well said, me too x
That's probably the ideal situation. If a tutor were to customize a lesson for you specifically, they'd probably aim for a difficulty level you'd find interesting, and a lecture that you could mostly follow. You'd also be very slightly outside your comfort zone, to give you room to "grow into" the lesson. It would also be a bit challenging and would leave you with a few questions to mull over, thereby slightly increasing the chance of watching another video, or of reading a book or article on a similar topic. Your comment would probably be music to the ears of a lot of educators.
@@shadowpresident4203 thx
I feel your pain! I truly do....
The fact that “chaos theory” is a real thing absolutely blows my mind. Even pure chaos can be mathematically modeled. Incredible.
The point of it is that chaos can’t be modeled but that it comes from that which can be modeled
TH-cam algorithm -
1st stage - sends to people who are actually interested in math. Less views
2nd stage - sends to related viewers. Less views but still constant.
3 stage - Sends to random people on their feed. Fluctuations in view cycle (no negative views so it shoots up)
4 stage (chaos) - recommends to people like me of all people. Millions of views
top comment!!
This observation is actually clever, considering that the algo is an AI
Recursive view count increases!
TH-cam's algorithm decode!
Stage 5: people in the Mandelbrot set
2019:- so this is aerogel
2020:- let's throw a little chaos at children and each other
Roshni Rana aqq msm
Chaos is magic.
Hey we have the same last name, first time I've meet one online
My apologies! if you are not interested in my offer I am from Russia .I live in Siberia looking for a sponsor (investor), please send this information to interested parties and companies..Thank you for reading with respect Popov Gennady.
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Still
I ask all people who are not indifferent to the problem! convey this message to interested parties and companies...
I found this incredibly fascinating... but understood incredibly little.
I was interested in it but i will always hate math cuz ths made me fall asleep lol
I understood more than I want, but still less
Yup! Make me want to go learn some math!
I had to write some things down to look up definitions! But interesting
Fibonacci equation.
I got chills watching this. Math is beautiful. Thank you for making this video.
This feels like a window into a small part of how the universe works. Its kind of scary and exciting.
Yeah it's very strange... all these formulas that pop up everywhere. I think there's an explanation though.
@@robologo have u tried psychedelic drugs? you actually start seeing these everywhere
@@pablooo8280 nobody has because drugs aren't real.
@@pablooo8280 no
@@mysonandme8424 yes
This is like when you start a new project or new year resolution. Everything is fine and simple at first, then progressively and unexpectedly everything turn to chaos
Probably the rate of degradation is 4.669 :o
This video taught me how hard is it to slightly open a tap...
lmao
This video certainly “open slightly” very well.
I ran across this video about a month into my discrete dynamical systems course. It has been super helpful to have something that gave me some intuition surrounding these patterns before I encountered them formally in class. Sharing it with my professor now :)
i think this was really interesting, i cant be sure as i didnt understand after hello
hahaha trueeee
😂🤣
Oh no, u is deaf?
Same here...
lmaoo same hahha
I saw the video title and thought “oh suuuuure this will change my life”, but wow I did not expect to be so taken aback by this. Something so fundamental which I’ve never heard about before!
Shilpan Patel so you should subscribe to numberphile
Sometimes, I feel like I can't even comprehend the almost divine beauty of math. You blew my mind a couple of times in this video...
Anki math is created by humanity
Therefore not divine bro. Don’t forge to pick up your Quran bro 😖 bless
@@gickygackers wtf?
Murica Presents huh
@@Insultthumb I think he means "god did it"...or some such rubbish
I watch this every single time I think about this concept. To be honest, one of the best decisions ever to beat this into my head. thank you for making this.
14:00 I played with this when I was younger and was fascinated to hear the different rhythms it makes. And here I am a decade later learning about it on youtube.
Fastest 18 minutes of my life. I think I actually found what I want to be when I want to grow up. A mathematician
Ha
Ha
Ha
Do it 👍 Maths is the supreme language of the universe. If you wanna understand the universe, math is the way. I embark on the same path and it's amazing
Manamrit Singh not really, mathematics is an abstract concept and it won’t make you understand the universe. It is more of a tool that you can use to „understand” the universe through physics. I know several brilliant mathematicians who decided to study physics when they understood the difference. Mathematics is not really that interesting when it comes to studying it. It’s the same as learning about black holes in physics, it’s a very brief lecture compared to other stuff that might seem boring like mechanics, kinematics, rigid bodies, aerodynamics etc.
What if you don’t want to grow up lolll
Don't let other people ever dissuade you from doing something you find passion for.
Me: cannot do basic calculus
*sees title of video*
TH-cam just gets me.
I taught myself basic calculus from videos on TH-cam. Both Khan Acad and 3blue1brown really helped. I was able to skip Math 251 (Calc 1) at my college and move straight to Calc 2 after a 4-year break between studying BASIC algebra in high school and returning to college.
@@BudEnzo wait what, you studied basic algebra in high school?
@@tishafeed8085 I guess lol. My school called it pre-calculus so basically it was algebra+trig.
@@BudEnzo what years/classes? in my highschool (9th-11th year) we did trig+calculus
@gamecube.enthusiast - - i did, but the fundamentals were studied in years 5-9, then it was trigonometry and calculus. Actually, i just realised it depends on what you call 'highschool'
I've been studying emergent behavior since the 80's, when I first read Conway's Game of Life.
Back then, it was treated as a nuisance, irrelevant, and annoying.
I love watching the break into oscillation as your R-value changes .That's the same behavior as a damped spring, or feedback in an audio system.
The transition to chaos between states makes a lot of sense.
I love the visualization of the Mandelbrot set, that gave me the perfect starting point to understand it in another dimension. Wonderful.
13:56 What really is a faucet? Hey, VSauce! Michael here
Somehow this relation never ceases to intrigue me
I actually didn't know what a faucet is...
Why is the water bill so high?
Me: Adjusting the tap into chaos
Chaos is a ladder
L.O.L, same.
@@GarmagaramAnday Peter baleish
Nice lol
The Government+Nestle= Screw You. Pretty easy equation.
He could have made all of that up and I would never know...
lol, I can tell it's true, chaotic equations do exists, however it's funny how the father of chaos theory wasn't even a mathematician, he was a meteorologist.
I lolled from the heart
You can just use matlab, duh
That is the scary part of learning on TH-cam. Thankfully he provides a lot of references :) I avoid taking information from TH-camrs as facts unless they can back it up
Hahahahahaha
That book is amazing - and you have done it justice. That 3d graph was awesome!
Do you know which software did he use?
This man can calculate almost everything. The one thing he can't do is calculate a 16 : 9 aspect ratio.
you gave me a good laugh LOL
ItsATurtle that’s hilarious
haha! i am watching this in ultrawide and I am grateful for this video! it goes almost to the edges of my screen and it made me pre
@@jebbbungo7873 Same, it's one of the very first videos to actually fit my screen perfectly and it's sooooo satisfying
He is cinematic that way.
You may have broken my amount of mind-blows in one video - the z-axis of the Mandelbrot set? The chaos of Bifurcation? The bifurcation constant? The practical applications? Incredible!!
One thing he didn't mention...there's a second Feigenbaum constant.
Not just the length of the tine with its subtine 4.669, but the width of the subtine 2.502
I barely understand this at 15 years old but I have a feeling I'll grow into it
@@akshatshah3717 maybe it will grow into you...
that 3D fractal diagram of the mandelbrot set expanded into its bifurcation expressing form in space, I've seen it before this video, and almost comprehended its nature, but now i see it clearly. and it's so beautiful. that is the single most beautiful object that mathematics has given us.
i want to give it a more poetic title that does it justice.
im thinking "The Mandelbaum Chaos Flower".
The more I learn, the more I realize I don't really know anything!
Ah, so you really have been paying attention! That seems to be one of the more important lessons to learn in life. So, here’s to you, me, and everyone else realizing we know less and less each year! 😀
@@mdestwo Well said!
That's for sure. I always think I'm smart, but a year later I always remember how stupid and dumb I was, and it keeps repeating
Exactly man. But now I'm 100% convinced that I know absolutely nothing.
welcome to the club! :D
Feels like when you are using exponential equations your inputs are very important and deserve a lot of explaining why you chose it, regardless of real value or best estimate value
I used to notice my sink doing this when I was a small child and always wondered what the heck was going on. This video just solved a 15 year old mystery for me. Thank you!
Yeah, but did it actually ... ?🧐
I did not even realise how quickly 18mins passed by.
Love you vertasium I want to grow up and do research and share on TH-cam just like you . You and Physics Girl are my favourite youtubers
If you're not aware of PBS Space Time, give them a watch, too. If that's too heavy, check out Isaac Arthur. If you're more into physical experiments, Applied Science or Practical Engineering are great channels. Of course, Numberphile, Sixty Symbols, Periodic Videos, and the rest of Brady Haran's channels are all good, too.
Nice choices my friend! Hopefully you already know the channels Smartereveryday and SteveMould. If you like Derek then you'll enjoy these guys too I hope.
Ikr? Almost at the end of the video, I had to scroll up and check you weren't joking, that felt like about 5 minutes...
Like 9 minutes in and it feels like 2 hours lol
Apple 2 never give up!! Study hard in school and you will do great things
When i had numerical maths in my University, there was a alot of chaotic stuff we came along and philosophised with our Professor about. Was one of the best classes I ever had
@earthly firefly5 Amen :)
Math professors are a lot more mystical than people give them credit for. When I took Calc II in college, I went to my prof and talked about the weirdness of infinity. I don't remember exactly what I said, but he got the funniest look in his eyes and said something like" in many ways, that is the great mystery behind all reality." Then I realized that if you spend your whole life studying math, it must really change your perspective on everything. Peering down into an endless sea of perfectly tuned complexity that most people never think about, and wondering why it's there or where it comes from...sheesh.
Your videos never failed to make me think about what is the purpose of this universe.. why is it there and how it works so perfectly without anyone controlling it..
You’ve re-kindled the magic! I read “Chaos” thirty years ago. It changed the way I see the world / time / history / physics. Please keep following this path ... you are blowing my 63 y.o. Mind! Thank you!
@@arnietapp423 lol what
@@arnietapp423 Ohhh, I see. Thank you for explaining.
@@arnietapp423 No, Sorry.
Nobody is. :P:D
th-cam.com/video/9Pvr-z6OKgw/w-d-xo.html
I love how genuinely excited he is about the topics he covers.
yup
True. He really deserve it for all this dedication and interrest into every movie.
I wish math was taught this way when I was a kid. We did a lot of one thing at a time (sausage stuffing, as we call it in Sweden :), but never got the explanations of their relations and that you can express something in many different ways with graphs, trigonometry etc. Granted, I chose the humanities side of studies later on; but if my teacher showed that an equation can be found within the Mandelbrot set or how you can represent it in many different ways, I think it would have created a lot more interest. This was a couple of decades ago, but still I wish my teachers had just scratched the surface of what lies beneath the "repeat this type of equation until your eyes bleed".
Time to go out and shout at kids about how things were better yesteryear and that we only had tape recorders to store data on and 8-bit consoles. And, of course, that we walked 8 km either way to school, uphill in both directions with snow all year 'round.
Ha! We say sausage stuffing in Portugal too
math teacher usually sucks at their major
You're also expecting the teachers to understand this subject and teach it. Unfortunately most teachers just regurgitate what's in the "teachers manual"
@@deman817 I have a couple of friends who are teachers, and the level of education they have to reach to be "certified" is way above what they teach. I guess it's a question of enjoying your work. You are definitly on to something though; the difference between an Office space-type and Dead poets society teacher is quite broad :) Also, at least locally, the work of education is relatively low paying. I'm probably naive in thinking it should be a kind of important thing no matter if the school is private or public. Money, money, money.
But now it's time to go out and tell the kids of today how we used to play with twigs and cones; and we had so much fun! They don't know how good they have it today... *mumbles about the price of milk*
The real truth that they don't tell you is that 99% of math in school is building up to one thing ... and that is Calculus. It's this that is important above all and gives you 99.9% of the things you have in the world. That's the main connection/secret that is missing.
Beyond excellent. One fascinating detail left out is the appearance of _intermittency_ a bit past 3.8
I am so glad that some lad just woke up one day and decided: "You know what, I should do some research of dripping faucet."
That would be a lad that doesn't get government funding.
weed is good for some things...
You mean, instead of fixing it?
you mean "woken up by a dripping faucet"?
Me: That was fascinating and mind blowing.
Me again: What did I understand from this video is that after rabbit, everything was chaotic.
Raw...bit ?
Joke?
so thats what "going down the rabbit hole" means. Descend into chaos
@@ironchump1501 no, dude, no, it doesn't. so...there, take that.
The battle between order and chaos continues.
When the Mandelbrot set rotates: whooaaaahhhhh
5erif meme echoes in my head...
Right!?!?!!
Yeh that was spectacular
"You're not supposed to do that!"
I swear to god, my mind was blown away by that! I had only ever seen the Mandelbrot Set as that 2 dimensional boundary thing, so seeing that it was actually a 3D-thing was insane
One of the most mind-bending concept I have came across. I love your channel, it is one of the best.
After watching this video I realized that math wasn't the subject I didn't like or found interesting. Math teacher was the subject I didn't like or found interesting.
for me it was the sheer work and repetetiveness of the exercises
Same, when I began they wanted to hold me back a whole year, yet when I was in 8th grade they refused to let me go to Highschool since I had finished all their math classes, so I had to take the same class over again. And they wonder why kids start smoking pot... I learned I hate the school system. They also had this space program for the gifted, and of course I was not invited in the beginning even though I was interested, they invited my only friend, and I asked, but they almost laughed at me. A couple years later in 5th grade they asked me if I would join, gave me a tour that was terribly underwhelming, so I explained and declined. Then in Highschool AP math the teacher yelled at me for asking a question he proclaimed was a stupid question in front of the whole class and refused to answer it even though he preached there are no stupid questions, totally making a fool of me. I dropped out and went to art Highschool, which was amazing. I went to community college for academics and even got college credit knocking off two credits for one course. Later the school begged me to come back because I took their tennis team to state as a freshman, but I couldn’t deal with their BS anymore. The best teacher I had for academics was a drunk history teacher, loved him, was passionate and I actually learned because he cared about history. I hear schools have only gotten worse in the last 25 years, but good thing we have such a massive military that you hardly need a Highschool education for. We really need to pay our teachers more!
M D Same. And, I have to check my OWN work with an answer book. How motivating to ‘legitimately’ do all of the exercises, they are very boring.
Not really. All these are based on more elementary mathematics you learnt in school (from elementary all the way to university) that requires "repetitive and boring" work. You can't dive into this interesting topic without a solid foundation, and the way to be good at everything is the same: you have to do it repetitively (though great intelligence is also crucial for a subject such as Mathematics). If you can understand all the theorems/methods/formulas on the first look and can remember them without repetitive practices, then you are a genius and you should absolutely choose a more suitable path for you. Yet I doubt many people have that capability.
@@evdm7482 I guess your anecdote deserves a counter anecdote. It was joining the military (to get money to go to college) and the military forcing me to learn logarithms and trig in order to calculate great circle distances (by hand no calculator just log and trig charts) and azimuths for HF radio operations that showed to me that math was fun, interesting, and useful. It led me to not only a career in the military (enlisted, not officer) but also to pursue a degree in math upon my military retirement. I am now a high school math teacher.
I had great teachers in high school, I went to a great school. I just wasn't interested in academics at that time in my life. It was the military that taught me to learn and to succeed at academics and other things in life. What I really needed was someone in my face, yelling at me, to challenge me. All I got in high school was platitudes and the usual "touch feely" BS that most teachers give to students. I had too many female teachers who really couldn't relate to the inner warrior of (many) male students. I think a few good male teachers could have made the difference for me, but I only had (mostly) female teachers. Now that I'm a teacher I know that my teachers weren't bad (at instruction), just incapable of reaching all students. I'm sure I'm guilty of this as well, I'm never going to reach all students. This is the one of the many drawbacks to collective education.
I offer this counter anecdote not as a critique of your comment but to show (in anecdotal form) that it was the military that made me a math teacher and that it was high school level math that I used in the military that has guided my journey.
I'm 27, and I'm glad I didn't have to wait 10 more years to find out about this
Same
Numberphile shared this in 2017.
And I'm 18, and I'm glad I didn't have to wait 19 more years to find out about this
i’m 17 haha
I’m 17 and glad i didn’t have to wait 20! Hahaha
I love that you mentioned that things like this should be taught to students. I completely agree!! Topics like this are why I started to be so interested in mathematics.
Yes! Math was so very dry in school- as if it was intentionally designed to be so. This presentation would have made math so more interesting had it been included in the curriculum.
Sad part is, you'd still get the usual "What will we ever need this for?!" in probably 95% of classes.
@@xXBenutzer235Xx yes…I taught HS for 10 years and got asked that question all the time.
Mathematics is pretty cool tbh- it's just the educational institutes and some dumbass tchrs who made it seem not-so-cool-thing...
So much intelligence, so much creativity and all that comes crashing down when we get to religion
Billions follow Master/Slave religions - "we must get down on our knees, swear loyalty & obedience to the Master & only to this master, he will be pleased & keep us in comfort(heaven)"
Simple, primitive ideas from simple primitive people being blindly followed by even the best of minds
Dude I have absolutely no idea of anything I just heard but I still listened all the way through it takes a very talented type of person to intrigue his audience that much.
Veritasium: "Students can have a little chaos, as a treat."
literally my teaching strategy
*little a chaos
If you're gonna reference the meme, at least do it right. It's "little a", not "a little".
Make them climb a ladder for it, though
Ben Gardner *le sigh* He DID say pedants were necessary..
I love how this converges to the VALUE of the Mandlebrot set at each point. I've often seen the drawing of where the set has valid values, but never thought about the values it holds in those areas.
I believe that in those videos of the Mandelbrot set where they zoom in for a long time, all the wild and crazy colors come from the value of the point as well. So visualizing the values in 3D space produces the logistic map with all sorts of chaotic lines, but visualizing the values with color produces a bunch of chaotic color patterns!
“When this baby rotates on the z-axis, you’re gonna see some serious sh*t.” - Dr. Emmett Brown
We don't talk about the Doc, since he f**ked up the timeline for 2020.
Wow doc.. that's heavy
@@davememelandcanada6722 I don't think that was doc.. I think that was biff when he stole the DeLorean
wht is z asix
@@anasaamir5595 If I had to guess it’s probably another axis like the y and x axis except it’s used for 3D shapes.
Great video! It's also a really good subject for a take-home final exam in a scientific computing class I am teaching this semester.
"How did I get to be 37 years old without hearing about the Feigenbaum constant?"
That is an extremely optimistic outlook on what 37-year-olds should be concerned about.
I turned 37 yesterday and I'm glad I've heard of it thanks to Derek
SomethingToJenga 100%
well im 7
Bina Shah good keep learning. You might be remembered for something awesome if stuff like this interests you!
jk im 13
Me: Watches video because I think I'm smart
My brain: Hold on there buckaroo
I feel attacked
Don't worry we're all retarded here. Welcome to the club.
Well how do you think (we) get smart?
LOL....You can actually apply the equation to your comment to see how funny your comment actually is! :)
Trevor Baylis no u cant
Dude, I'm halfway reading James Gleick's Chaos at the moment. The timing of your video's release is just perfect.
Oh, me too.
All praise The Almighty Algorithm!
It's the most omnipresent entity! It hears all. It sees all! and It recommends on your behalf.
001100
010010
011110
100001
101101
110011
I'm curious. May I ask what that is about?
Ayy got it on my shelf; I think I'll read it again
If you're looking for a good introductory text on the topic I'd highly recommend Exploring Chaos by Nina Hall and if you know what a Jacobian is and want to really get jiggy wit it then I'd suggest Strogatz.
I remember watching this video when I was about 14 years old and being fascinated by this, but my understanding kinda dropped off when the Mandelbrot Set came into the video (I knew nothing about it).
Rewatching this video at age 16, I can really appreciate it so much more, now that I understand it.
Thank you for introducing me to the Logistic Map!
I'm an electrical engineer in my master studies and had all this Mandelbrot in my third semester and I was so fascinated by it and you brought back the whole feeling of the universe being so mysterious and so logical but far over our understanding. Even in a century we may find new constants or similarities and still can not explain why. The best thing in science is not to understand the physics of the world or to use them but the exploration of things you do not understand, it's like seeing the best magic trick in the world. (and the universe is not gonna tell us how they cheated ;) )
Makes me think we're in an advanced simulation. 🤔
I feel smarter now, even though I still have no clue what he is talking about
me too :D
Same :”)
Sameee bro
Hahha
Couldn’t have said it any better😂
This made a lot more sense than I thought it would when I first watched it.
Eye-opening.
I agree, it's beautiful.
I LOVE this video and only now realised it was uploaded on my birthday :D