Predators and Prey - Numberphile

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  • Опубліковано 16 вер 2024

КОМЕНТАРІ • 683

  • @Skip_Sandwich_DX
    @Skip_Sandwich_DX 4 роки тому +554

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

    • @archivist17
      @archivist17 4 роки тому +15

      The reason I stopped using cursive...

    • @____-pb1lg
      @____-pb1lg 4 роки тому +10

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

    • @98081
      @98081 4 роки тому +8

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

    • @NoisqueVoaProduction
      @NoisqueVoaProduction 4 роки тому +7

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

    • @Skip_Sandwich_DX
      @Skip_Sandwich_DX 4 роки тому +19

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

  • @dougthedonkey1805
    @dougthedonkey1805 4 роки тому +606

    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
      @archivist17 4 роки тому +20

      Extremely hard to be content, too.

    • @lubieplacki2772
      @lubieplacki2772 4 роки тому +15

      @@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
      @oldcowbb 4 роки тому +3

      i can call this a trivial fact

    • @anthonygrow1482
      @anthonygrow1482 4 роки тому +8

      R/im14andthisisdeep

    • @wtspman
      @wtspman 4 роки тому +3

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

  • @b.a.r.c.l.a.y9701
    @b.a.r.c.l.a.y9701 4 роки тому +465

    all animals were harmed during the production of this video

    • @anuppokhrel2357
      @anuppokhrel2357 4 роки тому +5

      Only rabbits and foxes were harmed.

    • @jasper3706
      @jasper3706 4 роки тому +4

      Not the humans, I hope

    • @magran17
      @magran17 4 роки тому +6

      Call PETA. People Eating Tasty Animals.

    • @KuraIthys
      @KuraIthys 4 роки тому +2

      @@magran17 I prefer EEDP - Everyone Eating Defenseless Plants

    • @Triantalex
      @Triantalex 9 місяців тому

      false.

  • @DiracComb.7585
    @DiracComb.7585 4 роки тому +338

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

    • @williammedeiros2699
      @williammedeiros2699 4 роки тому +7

      Check 3blue1brown series on differential equations

    • @messinberver4683
      @messinberver4683 4 роки тому

      I'm doing differentiation and integration rn

    • @demenion3521
      @demenion3521 4 роки тому +4

      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
      @jpalacios117 4 роки тому

      Summr school go brrrr

    • @YourCrazyOverlord
      @YourCrazyOverlord 4 роки тому

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

  • @gametheory6948
    @gametheory6948 4 роки тому +278

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

    • @turdferguson3400
      @turdferguson3400 4 роки тому +17

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

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому +45

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

    • @abijo5052
      @abijo5052 3 роки тому +8

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

    • @rogerjohan9621
      @rogerjohan9621 3 роки тому +3

      @@TomRocksMaths Unless it is indeterminate...

    • @rafaelsoto4899
      @rafaelsoto4899 3 роки тому

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

  • @azhar07464
    @azhar07464 4 роки тому +309

    Ohh! The fluid dynamics guy.

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому +104

      That's me!

    • @Redditard
      @Redditard 4 роки тому +8

      @@TomRocksMaths I know right?

    • @Redditard
      @Redditard 4 роки тому +3

      Yass

    • @5hirtandtieler
      @5hirtandtieler 4 роки тому +6

      Tom Rocks Maths Got a new sub! 😊

    • @brunoc.3669
      @brunoc.3669 4 роки тому +4

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

  • @hamiltonianpathondodecahed5236
    @hamiltonianpathondodecahed5236 4 роки тому +253

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

    • @Albimar17
      @Albimar17 4 роки тому +9

      WHAT DOES THE FOXXX SAYYY?

    • @drenz1523
      @drenz1523 4 роки тому +8

      @@Albimar17 VVVVVVVVVVVVVVVVVVVVVVV

    • @sohee7597
      @sohee7597 3 роки тому +4

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

    • @Triantalex
      @Triantalex 9 місяців тому

      ??

  • @AlbiinoBlacksheep
    @AlbiinoBlacksheep 4 роки тому +45

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

  • @hotdogskid
    @hotdogskid 4 роки тому +20

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

    • @samayahone3497
      @samayahone3497 2 роки тому +1

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

  • @wobaguk
    @wobaguk 4 роки тому +212

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

    • @xevira
      @xevira 4 роки тому +27

      Revolution... around the steady state. :D

    • @aksela6912
      @aksela6912 4 роки тому +2

      Basically, the steady state here is the train in Snowpiercer

    • @kimon114
      @kimon114 4 роки тому +5

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

    • @jenm1
      @jenm1 4 роки тому +4

      @@kimon114 theres always a communist hater

    • @kimon114
      @kimon114 4 роки тому +4

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

  • @HasekuraIsuna
    @HasekuraIsuna 4 роки тому +222

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

    • @olmostgudinaf8100
      @olmostgudinaf8100 4 роки тому +55

      Because settling on one language is for the plebs.

    • @nicolascavadini3570
      @nicolascavadini3570 4 роки тому +9

      Exept japanese do not use latin alphabet

    • @alexv3357
      @alexv3357 4 роки тому +24

      @@nicolascavadini3570 Japanese uses romaji characters for many purposes

    • @EastBurningRed
      @EastBurningRed 4 роки тому +8

      u and v are the same letter in latin though

    • @tsuchan
      @tsuchan 4 роки тому +3

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

  • @My-Say
    @My-Say 4 роки тому +10

    OMG he's so cute :)

    • @archivist17
      @archivist17 4 роки тому +6

      Isn't he!

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому +3

    • @My-Say
      @My-Say 4 роки тому +2

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

  • @TomRocksMaths
    @TomRocksMaths 4 роки тому +7

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

  • @iteerrex8166
    @iteerrex8166 4 роки тому +14

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

  • @hcblue
    @hcblue 4 роки тому +12

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

  • @chuckvanderbildt
    @chuckvanderbildt 4 роки тому +81

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

    • @Mortiis558
      @Mortiis558 4 роки тому +4

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

    • @cmuller1441
      @cmuller1441 4 роки тому +11

      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
      @Mortiis558 4 роки тому +1

      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
      @TomRocksMaths 4 роки тому +4

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

  • @connoryoung1993
    @connoryoung1993 4 роки тому +7

    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!

  • @souptime8635
    @souptime8635 4 роки тому +75

    The intro gave me Monty Python vibes

    • @roderickwhitehead
      @roderickwhitehead 4 роки тому +16

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

    • @laurihei
      @laurihei 4 роки тому

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

    • @pdutube
      @pdutube 4 роки тому

      It *is* the rabbit!

  • @stevemarethyu3003
    @stevemarethyu3003 4 роки тому +8

    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.

  • @QuestionEverythingButWHY
    @QuestionEverythingButWHY 4 роки тому +61

    “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

  • @toopteeps6653
    @toopteeps6653 4 роки тому +25

    The man with the Navier Stokes Equation tattoo!

  • @nickcarter4006
    @nickcarter4006 4 роки тому +88

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

    • @murrfeeling
      @murrfeeling 4 роки тому +14

      "My degree is in math, not zoology."

    • @pierreabbat6157
      @pierreabbat6157 4 роки тому +9

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

    • @robertwynkoop7112
      @robertwynkoop7112 4 роки тому +7

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

    • @fewwiggle
      @fewwiggle 4 роки тому

      @Nick -- 2020 in nutshell

    • @DendrocnideMoroides
      @DendrocnideMoroides 4 роки тому +1

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

  • @amauryleblanc7979
    @amauryleblanc7979 4 роки тому +8

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

  • @nadya-catherineismail7804
    @nadya-catherineismail7804 4 роки тому +37

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

    • @R_V_
      @R_V_ 4 роки тому +4

      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
      @laharl2k 4 роки тому +3

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

    • @Toobula
      @Toobula 4 роки тому +5

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

    • @R_V_
      @R_V_ 4 роки тому +2

      @@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
      @hawkmoths 4 роки тому +3

      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.

  • @carlborgen
    @carlborgen 4 роки тому +22

    Expected to hear lotka-volterra being mentioned 🙈

  • @OlafDoschke
    @OlafDoschke 4 роки тому +46

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

    • @NoisqueVoaProduction
      @NoisqueVoaProduction 4 роки тому +13

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

    • @yomanxy
      @yomanxy 4 роки тому

      Woof or grrr?

    • @jasper3706
      @jasper3706 4 роки тому +4

      @@NoisqueVoaProduction *human screaming*

    • @Tfin
      @Tfin 4 роки тому +5

      (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.)

  • @SumNutOnU2b
    @SumNutOnU2b 4 роки тому +13

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

  • @zh84
    @zh84 4 роки тому +4

    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.

  • @xiaomarou9890
    @xiaomarou9890 4 роки тому +78

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

    • @himanshutahiliani1235
      @himanshutahiliani1235 4 роки тому

      Me too!!!!

    • @sachiel197
      @sachiel197 4 роки тому

      same

    • @stulebackery1363
      @stulebackery1363 4 роки тому

      yeah me as well

    • @bachirblackers7299
      @bachirblackers7299 4 роки тому +1

      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
      @PhilBagels 4 роки тому +2

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

  • @andywright8803
    @andywright8803 4 роки тому +7

    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.

  • @jackjensen422
    @jackjensen422 4 роки тому +11

    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?

  • @giosanchez2714
    @giosanchez2714 4 роки тому +14

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

  • @bachirblackers7299
    @bachirblackers7299 4 роки тому +4

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

  • @gigamungus5764
    @gigamungus5764 4 роки тому +17

    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
      @audreka13 4 роки тому

      ThatAwkwardGuy I think that’s intentional

    • @onecommunistboi
      @onecommunistboi 4 роки тому +2

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

    • @aakifaslam6098
      @aakifaslam6098 4 роки тому +3

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

    • @jon_j__
      @jon_j__ 4 роки тому

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

    • @cheeseboy8241
      @cheeseboy8241 4 роки тому

      @@onecommunistboi bless u

  • @Zolzulia
    @Zolzulia 4 роки тому +5

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

  • @Kaesekuchen002
    @Kaesekuchen002 4 роки тому +3

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

  • @archivist17
    @archivist17 4 роки тому +4

    More Tom please!

  • @GenericAnimeBoy
    @GenericAnimeBoy 4 роки тому +3

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

  • @avi12
    @avi12 4 роки тому +2

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

  • @5hirtandtieler
    @5hirtandtieler 4 роки тому +5

    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
      @TomRocksMaths 4 роки тому +1

      Thanks Tyler - glad you enjoyed it!

  • @RomanQrr
    @RomanQrr 4 роки тому +8

    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
      @Some.username.idk.0 4 роки тому

      Yup (also, one stable point)

    • @RomanQrr
      @RomanQrr 4 роки тому +2

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

    • @Some.username.idk.0
      @Some.username.idk.0 4 роки тому +1

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

    • @fatsteve3120
      @fatsteve3120 4 роки тому +1

      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!

  • @dougthedonkey1805
    @dougthedonkey1805 4 роки тому +12

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

  • @greyed
    @greyed 4 роки тому +3

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

  • @Johnnyb3g00d
    @Johnnyb3g00d 4 роки тому +2

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

  • @AeroCraftAviation
    @AeroCraftAviation 4 роки тому +6

    0:09 who caught the Wilhelm scream? 😂😂

  • @gmurphy1028
    @gmurphy1028 4 роки тому +27

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

  • @tsuchan
    @tsuchan 4 роки тому +2

    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.

  • @5445tashi
    @5445tashi 4 роки тому +2

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

  • @roseofthetree
    @roseofthetree 4 роки тому +3

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

  • @kevinfontanari
    @kevinfontanari 4 роки тому +73

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

    • @nottmjas
      @nottmjas 4 роки тому +9

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

    • @GiuocoPianissimo
      @GiuocoPianissimo 4 роки тому +5

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

    • @gregvandenberg2859
      @gregvandenberg2859 4 роки тому +4

      Run away!!!

    • @praneet6230
      @praneet6230 4 роки тому

      @@GiuocoPianissimo thinking the same thing lol

    • @amauryleblanc7979
      @amauryleblanc7979 4 роки тому +1

      2020 keeps getting weirder and of course, worse.

  • @SgtSupaman
    @SgtSupaman 4 роки тому +1

    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.

  • @skankhunt-zw6gg
    @skankhunt-zw6gg 3 роки тому

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

  • @Cosmic910
    @Cosmic910 3 роки тому +1

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

  • @jzieba0204
    @jzieba0204 4 роки тому +3

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

  • @itisALWAYSR.A.
    @itisALWAYSR.A. 4 роки тому +2

    Tom is so pure

  • @curlygurly2112
    @curlygurly2112 4 роки тому +5

    hello handsome mathematician 😳😳

  • @businessguide6219
    @businessguide6219 3 роки тому +1

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

  • @darekgala4667
    @darekgala4667 4 роки тому +4

    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

  • @whatskraken3886
    @whatskraken3886 4 роки тому +2

    this man is what i aspire to be

  • @EuphoricIntentions
    @EuphoricIntentions 2 роки тому +3

    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.

  • @CptFUBAR
    @CptFUBAR 4 роки тому +4

    The thumbnail at the end covered up the tattoo!!

  • @numberlife6470
    @numberlife6470 4 роки тому +4

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

  • @mrmojorisingii
    @mrmojorisingii 4 роки тому +37

    2:58 I think I've seen this meme before...

    • @DeivisAteivis
      @DeivisAteivis 4 роки тому +1

      AhAh!!!

    • @minewarz
      @minewarz 4 роки тому +2

      oh no

    • @hwiatslgeord2887
      @hwiatslgeord2887 4 роки тому +2

      Piper perrie meme

    • @thatoneguy9582
      @thatoneguy9582 4 роки тому +1

      I like how I didn't even have to click the timestamp to figure out exactly what you meant

    • @englishmotherfucker1058
      @englishmotherfucker1058 4 роки тому +1

      that looks like someone threw all those foxes at the rabbit while stooping time

  • @ajaisingh9129
    @ajaisingh9129 4 роки тому +1

    Love the animation at du/dt = u 😂😂😂

  • @xxMrPHDxx
    @xxMrPHDxx 4 роки тому +7

    8:52 Now I'm curious about that circular thing. I want a video on that

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому +9

      I'm planning to cover the extra detail on my channel soon - so keep your eyes peeled :)

    • @xxMrPHDxx
      @xxMrPHDxx 4 роки тому

      @@TomRocksMaths Cool. I'm so excited

    • @ryandean3162
      @ryandean3162 4 роки тому +2

      It's simply because any stable, repeating system of two variables in this way is either going to be constant, which would be the center point, which would make a straight line over time if you plotted it out, or it's going to vary in a regular fashion, which would be a sine wave, which means circular or at least ellipsoid. If you add in more variables, like the food source for the rabbits since they can easily devastate it if there's too many, or diseases like myxomatosis, or the fact that foxes have more prey than just rabbits, or a whole host of other real world considerations, you can get all sorts of weird lines and shapes that include things like a complete collapse of the feedback loop.

    • @upsydaysy3042
      @upsydaysy3042 4 роки тому +1

      @@TomRocksMaths aaaaaaand subscribed! First time ever I get any maths whatsoever. You are on another level.

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому

      @@upsydaysy3042 Amazing - you're very welcome :)

  • @YawnGod
    @YawnGod 4 роки тому

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

  • @suvamranjit7491
    @suvamranjit7491 4 роки тому +6

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

  • @demenion3521
    @demenion3521 4 роки тому +1

    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

  • @Quarky_
    @Quarky_ 4 роки тому +2

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

  • @SlimThrull
    @SlimThrull 4 роки тому +1

    "So we have a rabbit and a fox."
    0:52
    "So we have a rabbit and an anteater."

  • @vladimir520
    @vladimir520 4 роки тому +1

    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..)

  • @Tom-sp3gy
    @Tom-sp3gy 5 годин тому

    Thankyou so much !

  • @DumblyDorr
    @DumblyDorr 4 роки тому +4

    Did you just get through the whole video without mentioning the names "Lotka" and "Volterra" - or was I just not paying enough attention? :D

  • @rogerdearman
    @rogerdearman 4 роки тому +1

    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

  • @roseofthetree
    @roseofthetree 4 роки тому +2

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

  • @VivaanTheCraft3r
    @VivaanTheCraft3r 4 роки тому +3

    Yooo nice vid I understood everything 👍👍👍

    • @VivaanTheCraft3r
      @VivaanTheCraft3r 4 роки тому +1

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

  • @biktor75
    @biktor75 4 роки тому +1

    Lotka and Volterra, my heroes

  • @azlandpilotcar4450
    @azlandpilotcar4450 4 роки тому +1

    Rabbits eating foxes mathematically would be much simpler, but a much shorter video.

  • @rupen42
    @rupen42 4 роки тому +1

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

  • @user-vn7ce5ig1z
    @user-vn7ce5ig1z 4 роки тому +1

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

  • @dudedude7998
    @dudedude7998 4 роки тому +13

    he can teach me math any day of the week 😎

  • @princetyagii
    @princetyagii 4 роки тому +4

    The most stylish mathematician

  • @Mrfrog2024
    @Mrfrog2024 4 роки тому +25

    3b1b: I think I’ve seen this before

    • @wolfie6175
      @wolfie6175 4 роки тому

      Veritasium : me too !

    • @AlisterCountel
      @AlisterCountel 3 роки тому

      I’ve seen this one! This is a classic.
      >what you mean you’ve seen this? It’s brand new!

  • @sanjaytiwarytiwary6450
    @sanjaytiwarytiwary6450 4 роки тому +2

    2:59 is the best part

  • @doodelay
    @doodelay 4 роки тому +2

    6:41 Pokeball tattoos spotted :D

  • @basedblueboy8770
    @basedblueboy8770 4 роки тому +2

    I love his pokeball tattoos :)

  • @christiansrensen5958
    @christiansrensen5958 4 роки тому +2

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

  • @MusicFanatical1
    @MusicFanatical1 4 роки тому +1

    Wow I own two of the books behind him.

  • @PositronQ
    @PositronQ 4 роки тому +1

    This is also Computation and statistics

  • @jpalacios117
    @jpalacios117 4 роки тому +1

    That animator is fire. Keep him

  • @weber375
    @weber375 4 роки тому +11

    FIrst I thought: "Machine Gun Kelly is a Mathematician now?" then... "Sure, why not? If he saves Punk-Rock why not Maths too?"

    • @TomRocksMaths
      @TomRocksMaths 4 роки тому +4

      As a big punk-rock fan I will admit I am loving his new stuff!

  • @bachirblackers7299
    @bachirblackers7299 4 роки тому +2

    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

  • @trialbyicecream
    @trialbyicecream 4 роки тому +1

    Dang, that rabbit is cute!

  • @CorrectHorseBatteryStaple472
    @CorrectHorseBatteryStaple472 3 роки тому +1

    I'm a bit unconvinced by the equations. Might have been helpful to see the step where they take out the constants. I'm guessing the equations are "correct" but a lot got skipped...
    For example, you can't just say that more foxes = more competition = foxes die... There is only "competition" if there aren't enough rabbits to keep all the foxes fed.
    I'm guessing the foxes and rabbits were just the motivating example for this kind of analysis. Definitely a simpler approach than I was ever given at school.

  • @shriramsinkar8413
    @shriramsinkar8413 4 роки тому +2

    MGK on numberphile?? Interesting.

  • @felicityc
    @felicityc 4 роки тому +1

    being a fox i had a heart attack in the first five seconds...

  • @josebaurrestarazu1280
    @josebaurrestarazu1280 4 роки тому +1

    Great video!!!!

  • @koraptd6085
    @koraptd6085 4 роки тому +1

    14:00 the irony is the fact that modern meaning of word "kids" derives from term for the goat offspring that is usually killed by foxes ;p

  • @marshmelows
    @marshmelows 4 роки тому +1

    Brilliant video grasping the concepts of differential calculus!

  • @Wrutschgeluck
    @Wrutschgeluck 4 роки тому +1

    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