Math uses U and V to remind me how bad my handwriting is.

@archivist17

3 жыл бұрын

The reason I stopped using cursive...

@____-pb1lg

3 жыл бұрын

@@archivist17 bruh but in cursive you have the little curve on the v they don't look the same

@98081

3 жыл бұрын

My physics teacher always had us write U like ⨿ to make the difference clear.

@NoisqueVoaProduction

3 жыл бұрын

Wow,remembered my geometry class where the u,v and w were indistinguishable... By the teacher

@Skip_Sandwich_DX

3 жыл бұрын

@@NoisqueVoaProduction Now I'm taking actuarial exams where lower-case P, capital P, and Rho will be in the same equation representing different things.

u = 0 v = 0 “This is a happy place for the population” I mean, you can’t be unhappy if you don’t exist...

@archivist17

3 жыл бұрын

Extremely hard to be content, too.

@lubieplacki2772

3 жыл бұрын

@@archivist17 Satisfaction is made out of lack of deprivation, it only exists through a negative, like cleaniness is lack of filth. We need first to feel the thorn before we can enjoy its removal. Asymmetry.

@oldcowbb

3 жыл бұрын

i can call this a trivial fact

@anthonygrow1482

3 жыл бұрын

R/im14andthisisdeep

@wtspman

3 жыл бұрын

For the grass, this would be a very happy place.

all animals were harmed during the production of this video

@anuppokhrel2357

3 жыл бұрын

Only rabbits and foxes were harmed.

@jasper3706

3 жыл бұрын

Not the humans, I hope

@magran17

3 жыл бұрын

Call PETA. People Eating Tasty Animals.

@KuraIthys

3 жыл бұрын

@@magran17 I prefer EEDP - Everyone Eating Defenseless Plants

@Triantalex

8 ай бұрын

false.

I’m surprised how he explains differential calculus very well and is knowledgeable, but when it comes to rabbits everything falls to pieces

@turdferguson3400

3 жыл бұрын

I love how bad he is with words! They're going to.. erm.. populate like rabbits 😆🤣

@TomRocksMaths

3 жыл бұрын

As great as it is, a maths degree does have it's limits...

@abijo5052

3 жыл бұрын

@@TomRocksMaths how has no one picked up on this great pun yet

@rogerjohan9621

3 жыл бұрын

@@TomRocksMaths Unless it is indeterminate...

@rafaelsoto4899

3 жыл бұрын

@@TomRocksMaths tongue and cheek? “Limits”?🤪

As a man who’s taking a differential equations course, I gotta say the timing of this video so very convenient 👍

@williammedeiros2699

3 жыл бұрын

Check 3blue1brown series on differential equations

@messinberver4683

3 жыл бұрын

I'm doing differentiation and integration rn

@demenion3521

3 жыл бұрын

i'd say you rather find this in some course on nonlinear dynamics and not so often in a differential equations course. but maybe in this case, the equations might actually have a nice solution (didn't try to solve it)

@jpalacios117

3 жыл бұрын

Summr school go brrrr

@YourCrazyOverlord

3 жыл бұрын

You brave soul. This is the very maths problem that made me drop out of engineering.

Ohh! The fluid dynamics guy.

@TomRocksMaths

3 жыл бұрын

That's me!

@Redditard

3 жыл бұрын

@@TomRocksMaths I know right?

@Redditard

3 жыл бұрын

Yass

@5hirtandtieler

3 жыл бұрын

Tom Rocks Maths Got a new sub! 😊

@brunoc.3669

3 жыл бұрын

More than one, I guess the "change in the population of subscribers" is positive ;-)

5:18 "The change in u is equal to value of u." Peak wisdom.

@edwinvlasics4047

3 жыл бұрын

???? What's this supposed to mean

@alexandermcclure6185

4 ай бұрын

@@edwinvlasics4047 They are pretending "u" is the word, "you."

I love he can stumble over words and still sound smart lol very relatable

@samayahone3497

2 жыл бұрын

i dont know about relatable lol, if i stumble over my words i very quickly stop sounding smart xD

0:26 "u are going to represent the prey"

@Albimar17

3 жыл бұрын

WHAT DOES THE FOXXX SAYYY?

@drenz1523

3 жыл бұрын

@@Albimar17 VVVVVVVVVVVVVVVVVVVVVVV

@sohee7597

3 жыл бұрын

I misheard Brady's reply as "why me?"

@Triantalex

8 ай бұрын

??

It's kind of shocking how badly my professor bungled this explanation, and by contrast, how clearly this concept is laid out here.

@Mortiis558

3 жыл бұрын

Yeah this is where I got lost in calculus, same issue, bad prof explanation.

@cmuller1441

3 жыл бұрын

The difference between a video and a real course in Math is proofs. Here he just says: it goes arround the happy (1,1) point without even proving that the curves are closed! Couldn't those be spirals converging to the happy point or growing bigger and bigger? He draws things that looks like circles. He didn't even prove that the loops are convex... And of course those loops can't look like circles near the axes. In particular near 0,0 the curve cannot go down like a circle would do or you would cross the x axis...

@Mortiis558

3 жыл бұрын

c muller I am in particular referring to his explanation of dv/dt. I got integrating just fine but when dv/dt was introduced and included in integration I just lost the path and couldnt follow anymore.

@TomRocksMaths

3 жыл бұрын

Sorry to hear that Chuck, but glad I could help out :)

Can confirm I'm still looking for a carnivorous rabbit... any help much appreciated.

The "everyone's happy when there's nothing" case (v=0, u=0) just feels existential 😂

_u_ as in _usagi_ (rabbit in Japanese) _v_ as in _vulpes_ (fox in Latin)

@olmostgudinaf8100

3 жыл бұрын

Because settling on one language is for the plebs.

@nicolascavadini3570

3 жыл бұрын

Exept japanese do not use latin alphabet

@alexv3357

3 жыл бұрын

@@nicolascavadini3570 Japanese uses romaji characters for many purposes

@EastBurningRed

3 жыл бұрын

u and v are the same letter in latin though

@tsuchan

3 жыл бұрын

@@nicolascavadini3570 Really Nicolas? So for example, find me 'JVCKenwood' in Japanese characters. That's a famous enough Japanese company.

OMG he's so cute :)

@archivist17

3 жыл бұрын

Isn't he!

@TomRocksMaths

3 жыл бұрын

@My-Say

3 жыл бұрын

@@TomRocksMaths Oh wow, subscribed. :) I'm a little surprised you noticed my comment lol.

Mathematician: "Lets look at a steady state where EVERYBODY's happy..." Rabbits getting eaten to maintain status quo: "Revolution!"

@xevira

3 жыл бұрын

Revolution... around the steady state. :D

@aksela6912

3 жыл бұрын

Basically, the steady state here is the train in Snowpiercer

@kimon114

3 жыл бұрын

There is always a communist.... well he did not factor in the lettuce now, did he?

@jenm1

3 жыл бұрын

@@kimon114 theres always a communist hater

@kimon114

3 жыл бұрын

@@jenm1 There are no "communist haters" just people who understand communism.

The intro gave me Monty Python vibes

@roderickwhitehead

3 жыл бұрын

Well, that's no ordinary rabbit. That's the most foul, cruel, and bad-tempered rodent you ever set eyes on.

@laurihei

3 жыл бұрын

That is an ex-rabbit. That rabbit is no more. It's pushing up daisies.

@pdutube

3 жыл бұрын

It *is* the rabbit!

I think this single video has killed more rabbits and foxes than the rest of Numberphile content combined

I did a couple mathematical biology units for my undergrad. Tom, you explained this much better in 17 minutes and conveyed so much more than my lecturers did in two semesters!

@TomRocksMaths

3 жыл бұрын

Thanks Connor!

One of the beauties of maths.. Making sense of the quality and the quantity of complexity with ease.

I used to do a version of this with my fifth graders. It was for science/ecology, so we didn't get into the math, but it was a great way to show how connected everything in an ecosystem is.

this is one of the coolest looking maths nerd I ever saw on this channel

I recall a computer game that I played at school in about 7th grade, where you set up how many of each sort of animal you want in a population and then run a simulation, and it displays a 15x15 or so grid of animal sprites appearing and disappearing as predator-prey interactions play out over generations... Does anybody recall that game?

Which poses the final question: Are foxes red because of the carotin in the carrots the rabbits eat?

@NoisqueVoaProduction

3 жыл бұрын

I thought the ultimate question was : What does the fox say?

@yomanxy

3 жыл бұрын

Woof or grrr?

@jasper3706

3 жыл бұрын

@@NoisqueVoaProduction *human screaming*

@Tfin

3 жыл бұрын

(For anyone taking this seriously, the answer is "no." Well, it starts with that, anyway. It then goes on about Bugs Bunny and actual rabbit diets for a bit.)

The man with the Navier Stokes Equation tattoo!

@definitelydan2711

3 жыл бұрын

Yah he finally came with a new video I've been waiting for him 😂

@TomRocksMaths

3 жыл бұрын

Sure is :)

I very clearly remember doing a version of this when I was 15, writing endless results on a piece of paper and graphing the results as I went with lined paper and a bit of imagination. I was fascinated and had to tear myself away to revise my O levels.

his smile made this whole thing about eating rabbits and brutal law of nature, seem like casual goodnight story for kids

I first came across this in 1983, on a free tape of sample BASIC programs supplied with my Sinclair ZX Spectrum. This was called "Evolution, or Foxes and Rabbits", and you could type in the starting values for the two populations and then watch as they evolved in time.

Thomas is quickly becoming one of my faves on numberphile, he's so precious

@R_V_

3 жыл бұрын

Call me reactionary or anything, but his tattoos and piercings make me feel quite uncomfortable. I prefer hearing to his videos than watching them. Of course, it's just a personal distaste.

@laharl2k

3 жыл бұрын

He looks too "fabulous" doesnt he?....

@Toobula

3 жыл бұрын

I'm an oldie. It's the piercings I don't like. But I know I'm from a different time.

@R_V_

3 жыл бұрын

@@Toobula I may not be an oldie, but in a way I feel from a different time too. I'd say "from better times", but of course your mileage may vary.

@hawkmoths

3 жыл бұрын

I struggle to understand what his appearance, specifically a few small holes and a few tattoos, have to do with his ability to teach a concept effectively and make it enjoyable. But that's just me.

Expected to hear lotka-volterra being mentioned 🙈

@medore13

3 жыл бұрын

Me too :o

What i like about you most dr Rocks !!! Is your simple beautiful english and your smooth explanation . You are my favorite maths . Thanks prof .

@TomRocksMaths

3 жыл бұрын

It’s not rabbits eating foxes, it’s rabbit-eating-foxes

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. Science advances one funeral at a time.” ― Max Planck

@revimfadli4666

3 жыл бұрын

BuT bUrDeN oF pRoOf

That introduction was hysterical! The whole video was entertaining, as always. So glad to see him on your channel again!

@TomRocksMaths

3 жыл бұрын

Thanks Gio - more to come soon!

This video is worth watching! More of this, please!

Thanks for summarizing one of the first exercises I faced in Control Engineering

I just realized that from this explanation there are 3 types of starting points: points that are in the stable loop. points that lead to extinction, and points that lead to extinction of the foxes, while rabbits are booming.

@Some.username.idk.0

3 жыл бұрын

Yup (also, one stable point)

@RomanQrr

3 жыл бұрын

@@Some.username.idk.0 To be fair that's just a stable loop of a size 0.

@Some.username.idk.0

3 жыл бұрын

@@RomanQrr yeah, thats why "yup" was in the front of the sentence

@fatsteve3120

3 жыл бұрын

It might be worth looking at the Lotka-Volterra equations and how they precisely behave (as opposed to the somewhat simplistic drawing of the graphs presented in this video). As it turns out, unless there is an artificial, external extinction of either the predator population or the prey population, their populations can get infinitesimally close to zero and still recover!

As someone LITERALLY making a game using this as the core mechanic, the timing of this video cannot be any better 😂

Wow, I seriously wish I had the chance to watch this video back in highschool, this makes so much more sense.

When I saw “population of rabbits”, I immediately thought about the Feigenbaum-constant😅

@himanshutahiliani1235

3 жыл бұрын

Me too!!!!

@sachiel197

3 жыл бұрын

same

@stulebackery1363

3 жыл бұрын

yeah me as well

@bachirblackers7299

3 жыл бұрын

In fact still there is something to do with !!! Since it's about growth of two populations simultaneously in the same area ! Also we need to consider the nature is not only rabbit n fox ... There must be man n other creatures ... Plants .... Water ... Illness ... Death ... weakness ...

@PhilBagels

3 жыл бұрын

Yeah. I'm surprised he never mentioned the Logistic Function.

16:33 literally can't see what he's talking about because of the end screen cards lol, it pops up at the exact time and place to completely obscure the video

@audreka13

3 жыл бұрын

ThatAwkwardGuy I think that’s intentional

@onecommunistboi

3 жыл бұрын

Well because thats another video! If you want to see what hes talking about click on said end card:D

@aakifaslam6098

3 жыл бұрын

On mobile you just drag down on the video a bit and the cards disappear

@jon_j__

3 жыл бұрын

You can use the developer tools (F12 in firefox) to delete the overlay.

@cheeseboy8241

3 жыл бұрын

@@onecommunistboi bless u

Wow, what a beautiful connection between rabbit-fox population modeling and sine-cosine functions!

Brilliant video grasping the concepts of differential calculus!

"You are going to be the prey >:D"

@NoisqueVoaProduction

3 жыл бұрын

*Brady's breathing intensifies*

Really great, digestible video. I missed the nondimensionality at first, so was confused how a steady state was at [supposedly] (1 fox, 1 rabbit) but glad it was touched on and explained at the end :)

@TomRocksMaths

3 жыл бұрын

Thanks Tyler - glad you enjoyed it!

Great video!!!!

This was fun. Thanks!

“Rabbits eating foxes”??? RUNAWAY!! RUNAWAY

@murrfeeling

3 жыл бұрын

"My degree is in math, not zoology."

@pierreabbat6157

3 жыл бұрын

Rabbit: Let's switch roles for a while. Fox: Okay, I'm game.

@robertwynkoop7112

3 жыл бұрын

It’s just a rabbit...... I soiled my armor!......

@fewwiggle

3 жыл бұрын

@Nick -- 2020 in nutshell

@DendrocnideMoroides

3 жыл бұрын

@@murrfeeling but you have to know that "Rabbits eating foxes" is false

Tom was amazing! The fox/rabbit field animation at 01:01 was confusing because it didn't make sense it until I realised that it was misleading. It didn't include the 'lag' Tom talked about.

@TomRocksMaths

3 жыл бұрын

Thanks - glad you enjoyed it :)

More Tom please!

@TomRocksMaths

3 жыл бұрын

I'll be back don't worry!

I'm glad they clarified at the end, because I was definitely wondering how they expected any amount of rabbits less than 2 to keep reproducing and also how populations dropping below 1 didn't result in extinction.

0:09 who caught the Wilhelm scream? 😂😂

I remember doing this in uni! Such a nice way to remember what I used to do

I'm entering 11th grade, already kitted out with quite a lot of knowledge on mathematical analysis. Excited to learn it! (despite the pandemic, because of which I hope I'm taught analysis from home..)

I wonder if there is anything to the notion that a fox isn’t being drawn well, but a rabbit is. Also, the graph I think in regards to time, should be a wave with undefined portions in a peak and trough that extend to Infinity so that the flow of time isn’t interrupted.

when being confronted with such equations, i would start by looking at the nullclines (all the curves where one of the derivatives vanishes). this would give you the lines u=0, u=1, v=0 and v=1. and then you notice that the flow can only be perpendicular to the nullclines, so that you can kinda construct the circular behaviour. you still need to determine the direction of the flow at as least one point though (unless there are limiting cycles that separate the phase space). the only thing, you cannot determine that easily is the fact that you actually get circles here instead of spirals. that really requires linear stability analysis around the fixed points

the animation was really cool :)

this man is what i aspire to be

There's a really nice book for stability analysis: Introduction to Dynamics by Ian Percival and Derek Richards

Tom is so pure

Very elegant model which describes real life phenomena :) I wonder if this graph should look more like whirpool rather than circles? Populations will oscilate instead going towards equilibrium? :D

0:05 That's no ordinary rabbit! It's got huge--he can leap--LOOK AT THE BONES, MAN

Yeah, killer rabbits have started being a real problem recently...

@nottmjas

3 жыл бұрын

The solution would be to send for Brother Maynard and the Holy Hand Grenade of Antioch.

@GiuocoPianissimo

3 жыл бұрын

Not sure if this is a Re:Zero reference or a Monty Python reference.

@gregvandenberg2859

3 жыл бұрын

Run away!!!

@praneet6230

3 жыл бұрын

@@GiuocoPianissimo thinking the same thing lol

@amauryleblanc7979

3 жыл бұрын

2020 keeps getting weirder and of course, worse.

I saw you on Mike Boyd’s channel when he did the mathematics entrance exam to Oxford

That animator is fire. Keep him

6:$5- "And everybody's happy!" Well, except the rabbits that are being eaten.

I remember learning about it in biology class in primary school with the same graph in my textbook

he can teach me math any day of the week 😎

The thumbnail at the end covered up the tattoo!!

I learned about "daisy planet" yesterday, and then I get this video 😂

Great video: you should get him to explain Lanchester's laws next!

Yooo nice vid I understood everything 👍👍👍

@VivaanTheCraft3r

3 жыл бұрын

@Prabath Hemachandra Hey do you mind checking out my channel 😀

On the family ZX spectrum 48k there was an included cassette with some test software included (including a breakout\arkenoid clone amongst others), One of the included programs was a fox abbits simulation. Memories

This is an even better explanation of differencial equations than 3B1B's videos.

hello handsome mathematician 😳😳

@TomRocksMaths

3 жыл бұрын

I like this primate's colorful display pattern. It signals to predators that he is not a tasty meal. He is a clever primate.

Really cool, in our company we do the same thing, but with reflective light. Our diagram looks exactly the same: These two separate curves and as a result the circle :D

Wow amazing

Gorgeous, polite, funny and awesome at maths... my mother will definitely approve 😍😍😍

@TomRocksMaths

3 жыл бұрын

The predator/prey cycle where pop(PRED) lags pop(PREY) is a classic model. I first learned it from the Dewdney book _Armchair Universe._

Love the animation at du/dt = u 😂😂😂

This gave me a question. What is the difference between a vector field and a phase plane? My guess is that a phase plane is always is a circle that could be stretched like that, while a vector field can be anything, but I'm not sure.

@00:48, intriguing! He starts a drawing by first drawing the back of the object!!

The most stylish mathematician

@TomRocksMaths

3 жыл бұрын

He mentioned it in passing, but using u,v,w is very common for anything relating to differential equations

Interesting!

One the free bits of software that came with 16K Sinclair Spectrum was exactly this, you could set the initial state and got a graph produced on screen to show the populations, it was called Foxes and Rabbits.

Why there are exactly closed trajectories in the phase plane? There could be spirals, which arrows lead towards steady point (meaning it's asymptotically stable) or away from it (meaning its unstable)

"Rabbits are eating foxes" Re:zero s2 watchers: Understandable have a great day

and when is the Chaos coming? Next video? I like the way you examine the equations without resolved it. very impressive!

Finally somebody is making Dynamical system theory and Fluidynamics entertaining

This is a better illustration of whats happening in the Mendelbrot Set . What if we add more elements in the chain ... With multiple predators n preys . Always a number looks like he's chasing his squared Nr same as squaroot ... Thanks Dr

The host/parasite relationship between honey bees and varroa mites follow this same pattern. As the bees build up their Spring numbers the varroa mites lag behind, only peaking after the bee’s numbers begin to decline in autumn/winter. It is this lag that creates high mite numbers as the bee numbers seasonally decrease leading to colony morbidity - often in winter. 🐝

So cool

I love his pokeball tattoos :)

Damn son, i already knew this one from school but you kinda made it more intuietivly understandable! thank you!

@TomRocksMaths

3 жыл бұрын

You're very welcome :)

Great explanation. I would be interested in a video of a 3 species model.

@UCLAursinho

3 жыл бұрын

I referenced this paper back in college on the 3 species model. Great fun decades ago. Nonlinear Aspects of Competition Between Three Species | SIAM Journal on Applied Mathematics | Vol. 29, No. 2

hmm where did the circles come from? I think that couldve been given some more explanation.

Wow I own two of the books behind him.

Nice drawing!

Ohhh first time I saw mathematician with tattoo 👍👍😁😁😁