The Game You Can't Win

John Conway’s work stretched from nearly-inaccessible math theory to fun children’s games, and it defined how we thought about recreational mathematics in the 20th century. Conway’s Soldiers is the perfect example of a Conway-esque math game: the rules are simple, the gameplay is easy, and it becomes very hard very quickly… and in this case of a basic checkers game, it packs a surprising punch of becoming literally impossible for a reason that isn’t even close to obvious.
But the mathematical importance doesn’t end with an unexpected reveal of impossibility. Conway found that the secret to why it’s impossible depends on the Golden Ratio of 1.618, which has fascinated mathematicians since Pythagoras and Euclid. We see the Golden Ratio in aesthetically-pleasing magazine layouts, flower patterns, and pretty faces, but John Conway showed us that it’s at the heart of why we can’t reach the fifth row of a checker game.
Play the game yourself with the online simulator and check out Zvezdelina Stankova’s proof on Numberphile. It’ll make sense. John Conway may be gone now, but we’ll be playing his games and poring over his ideas for centuries.
Conway Checkers (proof), Numberphile2 | Zvezdelina Stankova: • Conway Checkers (proof...
Conway’s Soldiers Interactive Game (Clever Learning): www.cleverlearning.co.uk/blog...
** SOURCES **
Berlekamp, E. R.; Conway, J. H; and Guy, R. K. "The Solitaire Army." In Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, pp. 715-717 and 729, 1982.
Honsberger, Ross. "A Problem in Checker Jumping." Ch. 3 in Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 23-28, 1976.
Tatham, Simon and Taylor, Gareth. “Reaching Row Five in Solitaire Army.” tartarus.org/gareth/maths/stu...
plus magazine, “Mathematical Mysteries: The Solitaire Advance.” plus.maths.org/content/os/iss...
Bell, George. “The Peg Solitaire Army.” www.gibell.net/pegsolitaire/ar...
Bell, Hirschberg, Guerrero-Garcia. “The Minimum Size Required of a Solitaire Army.” arxiv.org/pdf/math/0612612.pdf
Taylor, Jasper. “Conway’s Soldiers.” sites.math.washington.edu/~mo...
John Conway’s obituary, New York Times: www.nytimes.com/2020/04/15/te...
Roberts, Siobhan. “Genius at Play: The Curious Mind of John Horton Conway” (2015). www.amazon.com/Genius-At-Play...
** LINKS **
Vsauce2:
Twitter: / vsaucetwo
Facebook: / vsaucetwo
Talk Vsauce2 in The Create Unknown Discord: / discord
Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research and Writing by Matthew Tabor
/ tabortcu
Editing by John Swan
/ @johnswanyt
Huge Thanks To Paula Lieber
www.etsy.com/shop/Craftality
"Binary Max Escape" by Basswaite: distrokid.com/hyperfollow/bas...
Select Music By Jake Chudnow: / jakechudnow
Get Vsauce's favorite science and math toys delivered to your door!
www.curiositybox.com/
#education #vsauce2 #maths

Пікірлер: 2 700

  • @anythingg00394
    @anythingg003944 жыл бұрын

    My guy really drew us a whole board just to tell us that he cant use it. The dedication.

  • @VivekYadav-ds8oz

    @VivekYadav-ds8oz

    4 жыл бұрын

    Was about to comment the same.

  • @GautierAuvin

    @GautierAuvin

    4 жыл бұрын

    It's not about the board, it's about sending a message

  • @nickcru5637

    @nickcru5637

    4 жыл бұрын

    Not stonks

  • @DMFM71

    @DMFM71

    4 жыл бұрын

    @@catwpants beautiful

  • @PhaseControlDNB

    @PhaseControlDNB

    4 жыл бұрын

    also - he wanted to show that 5th level is impossible but drew a 7-level board :D

  • @bunsenn5064
    @bunsenn50642 жыл бұрын

    I actually managed to win this game, I used a strategy called “cheating whenever I’m at a disadvantage”

  • @rayzorblader9198

    @rayzorblader9198

    2 жыл бұрын

    XD

  • @TimThomason

    @TimThomason

    2 жыл бұрын

    Yes, we can solve this if we bend the rules a little bit. Specifically the rules that say you have to jump other pieces. Or that you can't just put any piece on Row 5 from wherever.

  • @DotDotEight

    @DotDotEight

    2 жыл бұрын

    did you use wemod?

  • @wertwert225

    @wertwert225

    2 жыл бұрын

    lol nice

  • @quedoom

    @quedoom

    2 жыл бұрын

    Good job 👏

  • @brighton2862
    @brighton28623 жыл бұрын

    "The game you cant win" Me: pretty much every game i've ever played.

  • @dwijnapal4615

    @dwijnapal4615

    3 жыл бұрын

    Lol

  • @gaby8706

    @gaby8706

    2 жыл бұрын

    Lol

  • @Vota_

    @Vota_

    2 жыл бұрын

    Lol

  • @TheUnderscore_

    @TheUnderscore_

    2 жыл бұрын

    Lol

  • @evanderyorrel3549

    @evanderyorrel3549

    2 жыл бұрын

    Lol

  • @thomasfieschi-rose3705
    @thomasfieschi-rose37053 жыл бұрын

    Rest In Peace, John Conway. The man that gave us life.

  • @rogen8094

    @rogen8094

    2 жыл бұрын

    Uhh... I mean, he was a great man, but didn't give us "life" Unless he's your father - in which case - I'm sorry for your loss. EDIT: Yes, I get it now! Apologies for the dumb comment! ;)

  • @no-ls7uj

    @no-ls7uj

    2 жыл бұрын

    @@rogen8094 i mean technically he did cuz he made the game of life

  • @rogen8094

    @rogen8094

    2 жыл бұрын

    @@no-ls7uj Fair point!

  • @tabbeyond311

    @tabbeyond311

    2 жыл бұрын

    @@no-ls7uj yeha

  • @tabbeyond311

    @tabbeyond311

    2 жыл бұрын

    @@no-ls7uj i mean yeah

  • @jmzlolo
    @jmzlolo4 жыл бұрын

    Thanks for making a tribute to John Conway, I'm sure he would have appreciated it

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    @@OzoneTheLynx i didn't since i had sort by newest

  • @recklessroges

    @recklessroges

    4 жыл бұрын

    I'm not sure that he would have, but I certainly do.

  • @OzoneTheLynx

    @OzoneTheLynx

    4 жыл бұрын

    @Gaytony It wasn't originaly... When I looked there were quit a few comments before it.(many of which I suspect were from bots).

  • @gamingworld8355

    @gamingworld8355

    4 жыл бұрын

    R.I.P. John Conway

  • @AlexPBenton

    @AlexPBenton

    4 жыл бұрын

    It’s even better, because Conway hated being known only for Conway’s game of life, so discussing something he did that is lesser known is probably what he would have wanted.

  • @teridactyl1250
    @teridactyl12504 жыл бұрын

    ‘It’s like trying to invade Russia in winter’ *laughs in Mongolian*

  • @johnlang6500

    @johnlang6500

    4 жыл бұрын

    It's like trying to invade Russia in the winter - Impossible. Except for the Mongols!

  • @justinross4109

    @justinross4109

    4 жыл бұрын

    Cue the mongoltage

  • @christianlamb3911

    @christianlamb3911

    4 жыл бұрын

    Crash Course Gang

  • @teridactyl1250

    @teridactyl1250

    4 жыл бұрын

    @@justinross4109 well done

  • @jovicagasic98

    @jovicagasic98

    4 жыл бұрын

    I thought the exact same thing 😂😂😂

  • @ahuman3393
    @ahuman33933 жыл бұрын

    Every time I hear about Conway the guy sounds cooler, his game of life is still one of my favorite things

  • @Psi_Fan123

    @Psi_Fan123

    5 ай бұрын

    Game of life or?

  • @FrancisACNH
    @FrancisACNH3 жыл бұрын

    Kevin: “This video is spo-“ Me: *furiously taps right side of the screen*

  • @evaporatedmilkee6263

    @evaporatedmilkee6263

    3 жыл бұрын

    LOL

  • @adyhottie

    @adyhottie

    3 жыл бұрын

    Ngl mischif sounds really good for trolls.

  • @manwithabagon

    @manwithabagon

    3 жыл бұрын

    *with having it 60 seconds every two taps*

  • @garrylarry890

    @garrylarry890

    3 жыл бұрын

    What is the right side of the screen Oh. I got it

  • @cjfdnqkn4374

    @cjfdnqkn4374

    3 жыл бұрын

    mschf: no!!!!

  • @notsofast3748
    @notsofast37484 жыл бұрын

    Right? Wrong! :(

  • @qwertyqwerty9349

    @qwertyqwerty9349

    4 жыл бұрын

    Right!!

  • @gamingworld8355

    @gamingworld8355

    4 жыл бұрын

    @@qwertyqwerty9349 WRONG!!!

  • @hugo4049

    @hugo4049

    4 жыл бұрын

    Or is it?

  • @gamingworld8355

    @gamingworld8355

    4 жыл бұрын

    @@hugo4049 or Kinda just going with the flow

  • @hugo4049

    @hugo4049

    4 жыл бұрын

    @@gamingworld8355 Just forgot OR.

  • @cr4ckem
    @cr4ckem4 жыл бұрын

    I can imagine Kevin bullying his future child with the whole "right? WRONG!" thing. Poor kid.

  • @anduro7448

    @anduro7448

    4 жыл бұрын

    and one time he goes "right? yea , its right"

  • @retardedautist

    @retardedautist

    3 жыл бұрын

    He already has 23 babies

  • @anawesomepet

    @anawesomepet

    3 жыл бұрын

    @@retardedautist No, he has 70.

  • @mryodak

    @mryodak

    3 жыл бұрын

    "To get it right you would need to bend time. John Conway had imagined a group in the 196,883-dimensional space called a monster. And now, go to bed!"

  • @jackdaniels4968

    @jackdaniels4968

    3 жыл бұрын

    brutal

  • @trackeralias1124
    @trackeralias1124 Жыл бұрын

    2n+1 for the moves seems complicated.. if the goal is reached when the final piece hits the target level, and each move removes one piece, then you'll always make total pieces - 1 moves? as you can't have 'pieces left over' as any piece used effectively deletes itself.

  • @jax6648
    @jax66483 жыл бұрын

    “The goal of this game is to get these checkers to the other side of the li-“ Me: *shoves all the checkers to the other side of the board with my arm*

  • @augustomoreira7441

    @augustomoreira7441

    2 жыл бұрын

    instant win

  • @CanYouPeeInYourAss

    @CanYouPeeInYourAss

    2 жыл бұрын

    I know that this is a joke, but that's called cheating.

  • @coolj4334

    @coolj4334

    Жыл бұрын

    👍

  • @stm7810

    @stm7810

    Жыл бұрын

    Me: removes the line

  • @Sci0927

    @Sci0927

    Жыл бұрын

    Rotates board

  • @huhneat1076
    @huhneat10764 жыл бұрын

    This feels a lot like Minecraft piston extenders

  • @scottharbin1868

    @scottharbin1868

    4 жыл бұрын

    Tru

  • @Potatoboii2

    @Potatoboii2

    4 жыл бұрын

    You can make it 24 pistons

  • @cowch3916

    @cowch3916

    4 жыл бұрын

    Jing RS Lin ᴍᴄ it don’t work 😭 (the link)

  • @allovas

    @allovas

    4 жыл бұрын

    @@cowch3916 remove the space

  • @laurinneff4304

    @laurinneff4304

    4 жыл бұрын

    @@cowch3916 here: kzread.info/dash/bejne/g2aNtqVwXdSag6Q.html

  • @DrakiniteOfficial
    @DrakiniteOfficial4 жыл бұрын

    This is the first I heard about Conway's death. Rest in peace, my friend. You've done so much for us.

  • @JohnJohnson-od6dd

    @JohnJohnson-od6dd

    3 жыл бұрын

    Well thats part of the game .. The game of life (Insert laugh track here)

  • @ammaleslie509

    @ammaleslie509

    3 жыл бұрын

    maybe he can see the beautiful additional dimensions now

  • @cjfdnqkn4374

    @cjfdnqkn4374

    3 жыл бұрын

    R.I.P. Rest In Peace My friend Conway...

  • @the-anhpham3364

    @the-anhpham3364

    3 жыл бұрын

    Conway's Game of Life and Death

  • @Jst4vgApostle

    @Jst4vgApostle

    3 жыл бұрын

    Tbh I didn’t even know he was still alive (in 2019) until now...

  • @danieltreshner4955
    @danieltreshner49552 жыл бұрын

    The main difficulty I ran into using the game in the link, is that as you progress, you slowly create a void behind your leading soldier. That void prevents other soldiers from progressing in that column purely because they can't reach it.

  • @hadesciphernius5244

    @hadesciphernius5244

    Жыл бұрын

    Ah. The main difference between explaining something logically and mathematically.

  • @wren_.

    @wren_.

    8 ай бұрын

    It kind of feels like when you start running in a dream but you’re not actually going anywhere

  • @dukeofshadows5211

    @dukeofshadows5211

    7 ай бұрын

    Yeah this is what I discovered to get one to the 5th row you need one in the 4th with one in the 3rd also but once you get one in the 4th row the remaining tiles are 5+ rows away.

  • @spoopy2180
    @spoopy21803 жыл бұрын

    It's Like trying to invade russia in winter, its impossible *_heh im just glad hitler didnt know that_*

  • @SunflSeeds

    @SunflSeeds

    2 жыл бұрын

    He did and so he did it 6 months before winter but then he was too slow

  • @zettour.

    @zettour.

    2 жыл бұрын

    @@SunflSeeds Nah, he was just really confused that Stalin didn't surrender when Hitler marched into Moscow. Though, I guess Napolean was in the same exact situation centuries ago.

  • @bypy3544

    @bypy3544

    2 жыл бұрын

    @@zettour. napoleon waiting at moscow for tbe russiand to surrender A few montha later Brutal winter rekts napoleon

  • @woodybrison

    @woodybrison

    2 жыл бұрын

    There is a theory that Stalin goaded Hitler to invade. Fighting near your own land you don't have a long supply chain.

  • @ILoveNigga

    @ILoveNigga

    2 жыл бұрын

    Soviets and Mongols

  • @dorukefeozkan
    @dorukefeozkan4 жыл бұрын

    every actual time i watch a vsauce2 video: kevin: yes me: yes? kevin: no me: no? kevin: WRONG

  • @cjfdnqkn4374

    @cjfdnqkn4374

    3 жыл бұрын

    Me: brain explodes

  • @bonuswastaken

    @bonuswastaken

    2 жыл бұрын

    Second

  • @Itz_Sophia19

    @Itz_Sophia19

    2 жыл бұрын

    @@cjfdnqkn4374 same

  • @MrOvergryph
    @MrOvergryph4 жыл бұрын

    Kevin: "You can solve it if you bend time" Also Kevin: "Using 27-digit-dimensional space" Still Kevin: "He called it the Monster" *boldy explains nothing to audience* More Kevin: "And as always, Thanks for watching!"

  • @Piotr_Tokarz

    @Piotr_Tokarz

    4 жыл бұрын

    I am literally confusion

  • @tyzonemusic

    @tyzonemusic

    4 жыл бұрын

    The "you can solve it if you bend time" thing is a bit complex but very well explained in the paper in the desc tartarus.org/gareth/maths/stuff/solarmy.pdf

  • @vincentvanzwietenOFFICIAL

    @vincentvanzwietenOFFICIAL

    4 жыл бұрын

    @@tyzonemusic what I find interesting is that the solution literally uses all of the infinite soldiers to reach level 5.

  • @tyzonemusic

    @tyzonemusic

    4 жыл бұрын

    @@vincentvanzwietenOFFICIAL Yep! In the paper they mention a general version of the problem for N-dimensional checker boards, and have similar results. For a 3D checker board, you'd be able to reach a score of 7 with finite moves, and 8 with infinite moves (once again using every soldier).

  • @orlandomoreno6168

    @orlandomoreno6168

    4 жыл бұрын

    @@tyzonemusic transfinite numbers?

  • @SuperSoxGaming
    @SuperSoxGaming8 ай бұрын

    6:00 SAYONARA, PUNY CHECKER BOARD!!!

  • @xarim4769
    @xarim47693 жыл бұрын

    Kevin: mentions the golden ratio Me, an idiot that read JoJo: I’ve seen this one!

  • @Batmanman01

    @Batmanman01

    2 жыл бұрын

    exactly what i thought of

  • @kabirbatra
    @kabirbatra4 жыл бұрын

    I'm all sad now..I remember when I was super fascinated with Conway's game of life in middle school, and I remember when my 8th grade teacher told me she had actually met Conway in person and they were friends..and I was so amazed and wished I could meet him some day..what a weird feeling it is to know that he was just human, vulnerable to corona like the rest of us. May his beautiful lessons live forever in the mathematical community, and may his games continue to appeal to the interests of people of all ages, from cs students programming the game of life at school, to nerds watching Vsauce and Numberphile. Thanks for watching? More like thanks for making this video Kevin.

  • @duk8227

    @duk8227

    2 жыл бұрын

    Wait he died from corona?

  • @kabirbatra

    @kabirbatra

    2 жыл бұрын

    @@duk8227 10:06

  • @duk8227

    @duk8227

    2 жыл бұрын

    @@kabirbatra wow never knew he was an alcoholic...

  • @kaka88k1

    @kaka88k1

    2 жыл бұрын

    this is so emotional ):

  • @observr8390

    @observr8390

    2 жыл бұрын

    @@duk8227 how on earth did you derived that he is an alcoholic by using fact that he died of corona? are you one of the corona-deniers degenerates or something?

  • @joiscode3832
    @joiscode38322 жыл бұрын

    Rip, john conway, may he always keep inspiring and fascinating people with the games math and legend he left behind.

  • @davidmagyar6093
    @davidmagyar60933 жыл бұрын

    "It's like invading Russia in winter" Finland: Not impossible... Mongolia: Am I a joke to you?

  • @papertom

    @papertom

    2 жыл бұрын

    Germany: cries while doing so

  • @iamdivan7368

    @iamdivan7368

    2 жыл бұрын

    Poor Napoleon

  • @budd8852
    @budd88524 жыл бұрын

    Well of course you can't beat it. You haven't handed the controller to your older brother yet.

  • @arielsproul8811

    @arielsproul8811

    3 жыл бұрын

    I am the older brother, and this can be beaten by moving into hyperbolic space

  • @CopyTheCompcom

    @CopyTheCompcom

    3 жыл бұрын

    The disappointed chorus kid fits this comment

  • @masonhunter2748

    @masonhunter2748

    3 жыл бұрын

    Ariel Sproul nah you have to move into 12324587452 dimensional space and you need 2938737284 chips

  • @EclipsaEldrich

    @EclipsaEldrich

    3 жыл бұрын

    I’m the oldest, and I’ll tell you how. Ya gotta jump twice, duck twice, dash to the left then right then left then right, draw a b and a and write start.

  • @CopyTheCompcom

    @CopyTheCompcom

    3 жыл бұрын

    @@EclipsaEldrich That's cheating, dude!

  • @Never_Always2
    @Never_Always24 жыл бұрын

    “It becomes mathematically impossible which seems impossible” No way

  • @christianbarnay2499

    @christianbarnay2499

    4 жыл бұрын

    I think you missed the meaning of this sentence. He doesn't say that "Mathematically impossible" is almost the same as "Impossible". He says that the mathematically proven fact "You can't reach as far as you want even with an infinite supply of soldiers" seems impossible.

  • @Never_Always2

    @Never_Always2

    4 жыл бұрын

    Christian Barnay yep what’s your point?

  • @eljot1092

    @eljot1092

    4 жыл бұрын

    @@Never_Always2 his point is you missed the meaning of the sentence

  • @elfro1237

    @elfro1237

    3 жыл бұрын

    Oscar Ward he was not saying that something that was mathematically impossible was impossible. He was saying that it seems impossible that is is impossible, meaning it seems possible.

  • @markys_top1514
    @markys_top15142 жыл бұрын

    4:20 I think about "number of soldier"--1

  • @GabRioBlu

    @GabRioBlu

    6 ай бұрын

    yea its just 2^n - 1

  • @michaelestrada1972
    @michaelestrada19723 жыл бұрын

    "The game you can't win" You're telling me there's games I can win?

  • @sharif47
    @sharif474 жыл бұрын

    On the second half of the previous year, one of my friends came to me with the idea of implementing Conway's Game of Life as a Software Development project and we ended up implementing a very basic version (i.e. not very optimized) in Unity. One day, I showed him a Numberphile video of Conway explaining Game of Life and he was like, "He's still alive?" and I was like, "Of course, he is." I didn't even know he died until this video. RIP John Horton Conway. We'll miss you.

  • @somewhatBoring

    @somewhatBoring

    4 жыл бұрын

    R.I.P We'll miss you Mr Conway... Never will we forget, the greatest minds, now we'll see, how are the greatest minds of tomorrow...

  • @somewhatBoring

    @somewhatBoring

    4 жыл бұрын

    We miss you already, If only you succeed to making a key of immortality, before it was too late, and the virus, beat you through the fight. RIP.

  • @panferno3926
    @panferno39264 жыл бұрын

    Everytime i get here because the headline sounds like a bad app ad and everytime i get dragged into the abyss of math and it's true nature, and by that i dont mean bad school math. I'm talking about the pure fascinating logic behind every single formula, every single number and how simple math looks when you such cool way to bring in across.

  • @scottgagnon7528

    @scottgagnon7528

    4 жыл бұрын

    math is truly beautiful sometimes

  • @facundocadaa9020

    @facundocadaa9020

    4 жыл бұрын

    That's how mafia works. Download Mafia City NOW

  • @edelweiss9467

    @edelweiss9467

    4 жыл бұрын

    Almost everyone (myself included) don't fully understand just how greatly the math we know have been simplified and "dumbed down" that we'd even find the fact that there's extensive proof that 1+1 = 2 ludicrous.

  • @Alvionalx

    @Alvionalx

    4 жыл бұрын

    spam

  • @Alvionalx

    @Alvionalx

    4 жыл бұрын

    spam

  • @SopranoCheese
    @SopranoCheese3 жыл бұрын

    Kevin: *says golden ratio* People who know part 7 of JoJo: Ah, yes, infinity

  • @jotarokujo6858

    @jotarokujo6858

    3 жыл бұрын

    Arigato Gyro

  • @louisBrother1988
    @louisBrother19883 жыл бұрын

    That ending almost got me crying. May you rest in peace John Horton Conway.

  • @WarDaft
    @WarDaft4 жыл бұрын

    There's actually a pretty intuitive way to see why you stall out. I'm going to post this before listening to the explanation, and before morning coffee so I could (possibly) be wrong. Movement requires spending pieces. More importantly, it requires spending *nearby* pieces. Movement higher requires spending pieces that you had to pay to move up there, meaning those pieces themselves "cost" more. The cost ends up exponential in the distance you move, at least doubling for each additional square of range, but the number of pieces in your "accessible fuel pool" increases only quadratically with increasing travellable distance, and so you starve out. If everything was conveniently in the right place, it should exactly double for every step up, but nothing is ever convenient, so it probably costs more to really actually move them. You can obviously move at least 1 place, at cost 2 (using 2 pieces from below the line). There's 4 fuel available within 1 distance (orthogonally, or by Manhattan distance) of your starting point, so you can move at least 2 places (at cost at 4). There's 9 fuel within 2 distance, so you can move at least 3 places (at cost 8). There's 16 fuel within 3 places, so you can move at least 4 places (at cost at least 16). There's 25 fuel within 4 places... Not enough to move 5 places which costs at least 32. It gets even worse from there. 36 fuel within 5, but cost 64. 49 within 6, but cost 128. 64 fuel within 7, but cost 256. Distance 10 has 121 fuel but costs at least 2048. In 1 dimension, fuel is sparser and you can't even move up 2 places. In 3 dimensions, fuel is denser, and you can move father - but the cost is still exponential which eventually beats the cubic fuel availability of 3d. In fact, any finite dimension Euclidian space will eventually run out of accessible fuel. Even if you can move a piece by more than one space in a hop, or diagonally. In a hyperbolic space, you should be able to move an unlimited distance up, because you access to fuel increases exponentially with distance. Note: we live in a functionally Euclidian space, and it costs fuel to move things - including fuel. We live in a very complicated game of soldiers. Time to watch.

  • @WarDaft

    @WarDaft

    4 жыл бұрын

    Update: I ran through a simple thought experiment modification where you're allowed to stack as much fuel as you want on a given square, and the cost to reach a given height with ideally placed fuel is actually the Fibonacci sequence, rather than doubling! 1 piece at height 3 cost = 1 piece on height 1 + 1 piece on height 2. 1 piece at height 4 cost = 1 piece on height 3 + 1 piece on height 2. A piece at height n is height (n-1) + height (n-2), the same recurrence as the fibonacci sequence, whose successive terms (regardless of starting terms, as long as they're both positive) tend towards... The golden ratio! That's how that comes in. This is probably all explained right in the original paper proving it impossible. Which I should probably go read.

  • @Bloodsong13T

    @Bloodsong13T

    3 жыл бұрын

    @@WarDaft nice! thanks for the analysis and explanation.

  • @XIIchiron78

    @XIIchiron78

    3 жыл бұрын

    Bruh (That was a fantastic explanation, you have talent!)

  • @XIIchiron78

    @XIIchiron78

    3 жыл бұрын

    This is actually an analogue for Tsiolkovsky's rocket equation 🤯 you have to carry your fuel

  • @gayatribiswal5652

    @gayatribiswal5652

    3 жыл бұрын

    My mind has grown hyperbolically!

  • @crunchytee
    @crunchytee4 жыл бұрын

    *Beautiful tearjerker outro begins* "and as always tha..." *manscape lawnmower ad begins* "WHEN IT COMES TO TRIMMING YOUR BALLS ..." KZread, I beg you. Let us watch the outro in piece

  • @commie281

    @commie281

    3 жыл бұрын

    oh my god HA

  • @pigman6954

    @pigman6954

    3 жыл бұрын

    69 likes...nice

  • @DoctorBones1
    @DoctorBones17 ай бұрын

    Conway is my inspiration, i love the way he turns extremely complicated math concepts into interactive experiences.

  • @DaellusKnights
    @DaellusKnights2 жыл бұрын

    Conway's game of life has long since been one of my favorite hobbies for times when I just wanted to chill and not use my brain overmuch. I didn't know he had passed. RIP Mr Conway. You didn't know me, but you changed my life in many ways. 💖

  • @samarthkhandelwal5263
    @samarthkhandelwal52634 жыл бұрын

    Every Vsauce2 video: Starts of as a simple game but ends with a life-changing quote. One of my favourite creator.

  • @Johnny-Joseph
    @Johnny-Joseph4 жыл бұрын

    I was looking forwards to how he would explain the 5th level by removing time... alas, maybe next... time

  • @adb012

    @adb012

    4 жыл бұрын

    It can be done in an infinite number of moves. But is a "not so large infinity" (because infinities come in many sizes, like there are as many natural numbers as there are rational numbers, but quantity of real numbers is infinite times larger than those even when all these sets are infinite to begin with). So you can set up an algorithm (at least in theory, because in practice it can't be realized) where the first move takes one second, the second move takes 1/2 second, the 3rd move takes 1/4 second, the 4th move takes 1/8 second and, in general, the n-th move takes 1/2^(n-1) seconds, and by 2 seconds you are done in infinite moves. It's like the famous paradox: You can never reach a place that is 2 meters away because you always need to reach the half point of what remains first. So you first move 1 meter, then 1/2 meter, then 1/4 meter and so on and you never get there. Except... if you do the first 1 meter move in 1 second, the second 1/2 meter move in 1/2 second, the 3rd 1/4 meter move in 1/4 second and so on, you've made all the required infinite moves to reach 2 meters in 2 second. And that is how you actually can get from the bed to the bathroom at all. It is called "supertasks". Note however tat you can get to the bathroom because it does actually take less time to walk 1/4 the distance than 1/2 the distance. So that is a "possible" (in the real word) supertask. But in real life you cannot make that each following checker move takes 1/2 of the time it took the previous time forever, so solving this puzzle in infinite moves and finite time is impossible in practice. And by the way, reaching row 6 is impossible even in infinite moves. Infinite moves is barely enough to take just one soldier to the 5th row. Eve 2 soldiers to the 5th row is impossible (I think).

  • @Geigenzaehler

    @Geigenzaehler

    4 жыл бұрын

    @@adb012 Two soldiers on the fifth row is impossible. In fact, you have to use every single one of the soldiers below the line to get a soldier to the fifth row. After the infinite sequence of moves, there is only one soldier remaining.

  • @alexandrubragari1537

    @alexandrubragari1537

    4 жыл бұрын

    @@Geigenzaehler or you can divide the infinity in two equal parts and make run 2 algoritms at the same tims 1 for 1 half and the other for the other half of soldiers and you have 2 soldiers on 5 lel

  • @Geigenzaehler

    @Geigenzaehler

    4 жыл бұрын

    @@alexandrubragari1537 I know you are probably joking, but I still want to give a short analogy why that's not possible, if anybody is wondering: Imagine an infinite row of soldiers. First soldier is valued 1. Next one 1/2 then 1/4, 1/8, 1/16 ... If I add all the soldiers values, I get 2. But no soldier can be ignored. By your method we could now divide the infinite row of soldiers into two infinite parts. But guess what, the sum is still limited to 2. This is analogous to why there can only be one soldier on the fifth row.

  • @serraramayfield9230

    @serraramayfield9230

    4 жыл бұрын

    Geigenzähler Set theory doesn't follow common sense....wait a second. Aleph-0 number of soldiers = 1 soldier on level 5. What would aleph-1 soldiers get?

  • @livethefuture2492
    @livethefuture24923 жыл бұрын

    great video! and really loved the tribute to John Conway, R.I.P. truly a gem in this world!

  • @Mr_Tophatt
    @Mr_Tophatt Жыл бұрын

    "think of them as soldiers, trying to penetrate as deep as possible" well at this point I think I have won without playing

  • @DiogoCoutoooo
    @DiogoCoutoooo4 жыл бұрын

    Kevin: Right? Me: ye... Kevin: WRONG!!!...Kinda Later Kevin: so this is the perfect algorithm right Me: of cour... Kevin: WRONG!!!! Me: ... *of course it was wrong* ...

  • @Etrehumain123

    @Etrehumain123

    4 жыл бұрын

    Lol !

  • @TuxMan

    @TuxMan

    4 жыл бұрын

    Kevin : right? Me: *pauses* ... Me: r... i- Kevin: NOPE

  • @somewhatBoring

    @somewhatBoring

    4 жыл бұрын

    John died? The conway himself? 😥

  • @SCP--gr3pd

    @SCP--gr3pd

    3 жыл бұрын

    Kev: right? Me:... Kev:... Me... Kev:... Me:...y Kev:WRONG

  • @axlcodes
    @axlcodes4 жыл бұрын

    Absolutely loving that 12:34 video length!

  • @zsivkovicsmate8747

    @zsivkovicsmate8747

    4 жыл бұрын

    Because 5 is impossible

  • @confus.d

    @confus.d

    4 жыл бұрын

    WRONG!

  • @snl9500

    @snl9500

    9 ай бұрын

    it's 11:16 though

  • @AllShakhov
    @AllShakhov3 жыл бұрын

    "It’s like trying to invade Russia in winter" Actually literally everybody invaded in summer, but fought until winter. Забавно :D

  • @dragonmarble5779

    @dragonmarble5779

    2 жыл бұрын

    Да

  • @ERROR_account_lost.

    @ERROR_account_lost.

    2 жыл бұрын

    :D

  • @Wunba
    @Wunba2 жыл бұрын

    You can explain it all day, but I still won’t believe level 5 is impossible until I do it myself. 😂

  • @FabbeNJ369

    @FabbeNJ369

    Жыл бұрын

    Didn’t expect to see you here Wunba, love your videos

  • @Cowtymsmiesznego

    @Cowtymsmiesznego

    8 ай бұрын

    Well, that's understandable, as he didn't actually explain anything

  • @brotonnorgrinson7651

    @brotonnorgrinson7651

    6 ай бұрын

    Why are you here?

  • @loverofcattz932

    @loverofcattz932

    4 ай бұрын

    I sort of figured it out myself before he explained it, the soldiers will eventually run out of being close to the center line and you will not be able to get to that center line and keep going back and back until your too far away to do anything.

  • @3xtremelamborghini

    @3xtremelamborghini

    4 ай бұрын

    What are you doing here mister wunba

  • @raveneagle9117
    @raveneagle91174 жыл бұрын

    The dedication in this dude he drew a board just so he can’t use it

  • @irrelevant_noob

    @irrelevant_noob

    3 жыл бұрын

    And at 12:17 we get a glimpse of how LONG it really took to fill it up too... @-)

  • @pauldacon828

    @pauldacon828

    2 жыл бұрын

    The color of game pieces that he used makes me believe he was making a reference to Buddhist monks who spend hours, sometimes even weeks, making sand art just to sweep it all away in order to embrace the acceptance of the inevitably of the passage of time and the futility of trying to fight it.

  • @aarryasaraf
    @aarryasaraf4 жыл бұрын

    That man deserves this tribute and more rip JH Conway

  • @DaxSkrai
    @DaxSkrai2 жыл бұрын

    Instead of "2n+1" you could just say that it takes one less move than the number of pieces it takes to get to that level.. 8 pieces takes 7 moves to get to level 3.

  • @MiguelLopez-tj1br
    @MiguelLopez-tj1br2 жыл бұрын

    Got an essay to write about this for my calculus class thank you!!

  • @Pugs
    @Pugs4 жыл бұрын

    Is there ever going to be an actual POSSIBLE game?

  • @robertmorrison4457

    @robertmorrison4457

    4 жыл бұрын

    no

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    *NEVER!!*

  • @maxsteinbeezly7904

    @maxsteinbeezly7904

    4 жыл бұрын

    VSAUCE! Today I’m going to play Solitaire.

  • @shambosaha9727

    @shambosaha9727

    4 жыл бұрын

    Brussels Sprouts

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    @Tangent of circle. IMPOSSIBLE

  • @luis_leitao
    @luis_leitao4 жыл бұрын

    This video got insanely emotional all of a sudden, it was already really deep once you start feeling the frustration and the passion in Kevin's voice but the whole thing with John Conway got me real bad. I'm tearing up man, thanks for that.

  • @mr.jabbywock1830
    @mr.jabbywock18302 жыл бұрын

    3:52 trust me, and now you can't un hear it

  • @jaceysspace971
    @jaceysspace971 Жыл бұрын

    I don't understand any of this but I just listen to this man spit facts at my face

  • @2carrots25

    @2carrots25

    Жыл бұрын

    Same

  • @elucinadoboy4967
    @elucinadoboy49674 жыл бұрын

    wow, that ending really got me. Conway's death didn't really hit me until now. Thanks for helping carry on his legacy, Kevin

  • @adilloco6261
    @adilloco62614 жыл бұрын

    If a smart guy like kevin promotes an app it must be good Edit: just came back from the appstore the app is not available in my country so that is nice

  • @demerion

    @demerion

    4 жыл бұрын

    Same here :/ Gotte find an IPA or create a new account

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    @@demerion sad

  • @8o8inSquares

    @8o8inSquares

    4 жыл бұрын

    Same here..

  • @Johnny-Joseph

    @Johnny-Joseph

    4 жыл бұрын

    They must have paid him a tonne to drop his credibility like this

  • @syrialak101

    @syrialak101

    4 жыл бұрын

    @@Johnny-Joseph The app looks like it fits his style though.

  • @norman5917
    @norman59177 ай бұрын

    Bro i don’t usually tear up from stuff but for some reason I just started to get teary when he was talking about how Conway died.

  • @cubingman4632
    @cubingman46327 ай бұрын

    "One must imagine Sisyphus happy."

  • @ScibbieGames
    @ScibbieGames4 жыл бұрын

    Conway would be proud seeing something other than his Game of Life being talked about.

  • @razdahooman
    @razdahooman4 жыл бұрын

    WHAT???? he died??? I didn't even know and he was one of my favorite mathmaticians..... Really sad now :( hey, it was still a good video tho XD

  • @Mitiya__ua

    @Mitiya__ua

    4 жыл бұрын

    I didnt even know this guy before this video and now he is dead! Oh man! What is wrong to the world?need to cancel death for at least couple months

  • @saddlebag

    @saddlebag

    4 жыл бұрын

    @@Mitiya__ua I mean the main reason I knew about him was because of “Conway's Game of Life“ which he created.

  • @samraatplayz1607

    @samraatplayz1607

    3 жыл бұрын

    @@AbiGail-ok7fc Who

  • @RichTiger7
    @RichTiger7 Жыл бұрын

    "This is a one-player solitaire game." Thank you for the clarification. Otherwise, I might have become confused because of all the 4-player solitaire games out there.

  • @damamoot2291
    @damamoot229111 ай бұрын

    0:18 Two of the checker pieces swapped for some reason.

  • @AverytheCubanAmerican
    @AverytheCubanAmerican4 жыл бұрын

    Even if it doesn’t make sense, you have to admit that it’s kind of fun to do the impossible. Walt Disney said it best

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    Yup

  • @Ykulvaarlck
    @Ykulvaarlck4 жыл бұрын

    it's refreshing to see someone honor conway for one of his more interesting and significant discoveries, rather than the culturally-widespread one that i shall not name

  • @YahyaFalcon

    @YahyaFalcon

    4 жыл бұрын

    In case anyone doesn't know what yuval is referring to, it's the game of life

  • @wariolandgoldpiramid

    @wariolandgoldpiramid

    4 жыл бұрын

    Conway's Game of Life. You are not allowed to not name it.

  • @unhingedfrogspawn6715

    @unhingedfrogspawn6715

    4 жыл бұрын

    I am confusion

  • @anduro7448

    @anduro7448

    4 жыл бұрын

    @@wariolandgoldpiramid y tho?

  • @sujatapatne9521

    @sujatapatne9521

    3 жыл бұрын

    @@unhingedfrogspawn6715 y tho

  • @arcurifamily8525
    @arcurifamily85252 жыл бұрын

    Level 1, dirt, level 2, wood, level 3, Stone, level 4, bedrock

  • @pattsw
    @pattsw3 жыл бұрын

    I forgot that I was watching on 1.75x speed and wondered why Kevin was extra hyped up 🤣😅

  • @alandouglas2789

    @alandouglas2789

    2 жыл бұрын

    No you didn’t

  • @pattsw

    @pattsw

    2 жыл бұрын

    @@alandouglas2789 whatever you say 🤷‍♂️

  • @aldothelizard6669
    @aldothelizard66694 жыл бұрын

    Me: mom can we have "right" at home? Mom: we have "right" at home "right" at home: WRONG ! 1st thought, can you do it backwards, started it on a square at the 5th row 2nd thought, what if, the plane is 3 dimensional, so you have multiple column, row, AND layers; 1 checker can jump forward, backward, right, left, AND up and down

  • @YOM2_UB

    @YOM2_UB

    4 жыл бұрын

    On the second thought: level 5 would be fairly simple, just do level 4 like you do on the plane, then jump enough checkers down to do level 3 in the same spot. You could then jump enough checkers up to do level 4 again to get to level 6.

  • @user-wr2uy9pj4m

    @user-wr2uy9pj4m

    4 жыл бұрын

    Right? WRONG!

  • @adb012

    @adb012

    4 жыл бұрын

    "1st thought, can you do it backwards, started it on a square at the 5th row" You mean doing it in reverse? Like starting in the 5th row, jump back to the 3rd row and add a "soldier" in the 4th row? You can't make it in a finite number of moves. You will end up with soldiers "hanging" beyond the line and not being able to return.

  • @user-wr2uy9pj4m

    @user-wr2uy9pj4m

    4 жыл бұрын

    that's a really smart way to find a solution

  • @zsivkovicsmate8747

    @zsivkovicsmate8747

    4 жыл бұрын

    Actually if its over 2d, over 3d etc like 60d, its infinitely possible

  • @RicoEumaGreatestOfAllTime
    @RicoEumaGreatestOfAllTime4 жыл бұрын

    i'd like to get that "collar that swears when your dog barks "

  • @cornesalvo9366

    @cornesalvo9366

    3 жыл бұрын

    I have a really strong feeling that even though it's implied that the feet pic sending AI is worthless, a lot of people would think otherwise.

  • @hoyyosoy
    @hoyyosoy3 жыл бұрын

    One of the best videos I've seen, Kevin: we send you a big hug from Uruguay

  • @Infidak1ng
    @Infidak1ng3 жыл бұрын

    i felt like a hero when i reached the 4th tile until i realized that 5 was the impossible one

  • @seymourbutts5612
    @seymourbutts56124 жыл бұрын

    I love this tribute. Was so saddened to hear the news about Conway, but he’ll have a legacy unlike any other

  • @kandyappleview
    @kandyappleview4 жыл бұрын

    "The answer is beauty...and taxis." Sounds like me answering a word problem about trains on my math test

  • @MrSpooner1985
    @MrSpooner19853 жыл бұрын

    Playing the game, it quickly becomes apparent why you cant get to level 5; its so frustrating that each new tile you need is further back than use so you are always further and further away from the goal with tiles in front you can never reach again. Clever game.

  • @mfml94
    @mfml942 жыл бұрын

    Sometimes, I watch this video just to see the tribute that Jake made to Conway. It was very touching.

  • @kevinmyers8325
    @kevinmyers83254 жыл бұрын

    When you know kevin so well u can right wrong him before he does

  • @user-wr2uy9pj4m

    @user-wr2uy9pj4m

    4 жыл бұрын

    Right?

  • @pikach336

    @pikach336

    4 жыл бұрын

    WRONG

  • @CharlieBitMyFinger-bang
    @CharlieBitMyFinger-bang4 жыл бұрын

    - I'm sorry. I started drooling at about the 2:00 mark...t-t-t-TODAY, Junior!

  • @SuperSoxGaming
    @SuperSoxGaming9 ай бұрын

    I broke out into laughter when you said "SYAONARA, PUNY CHECKER BOARD!!" 😂

  • @thelearningcreator7makesmu614
    @thelearningcreator7makesmu6148 ай бұрын

    thanks for the existential crisis Vsauce

  • @fumpledump
    @fumpledump4 жыл бұрын

    When you make a custom board only to realize that the game is impossible...

  • @joshrobertson4900
    @joshrobertson49003 жыл бұрын

    This is the first news I've seen on John's passing. Thank you for the kind words.

  • @fbi3165
    @fbi31653 жыл бұрын

    I played that game .... i reached level 5 with my own board on paper..... How i got there was like a god making a barrier through the sea to make path..... So i was stuck at level 4 and the god came... my lil brother.... he was 7 and he solved how it was made my mind explode... When u reach 4 the "soldier" supposed to cant go further but my lil bro took 1 soldier and put it right behind the 4th soldier i asked why and he said " Why not" lol xD

  • @GhostlyGorgon
    @GhostlyGorgon7 ай бұрын

    The formula for the number of moves it takes is just the number of pieces - 1. This is easy to see because every move removes a piece

  • @jay-tbl
    @jay-tbl4 жыл бұрын

    fun fact: otters have a favorite rock they take around wherever they go edit: what? this comment is from two years ago and i neither remember making it nor watching this video. it isnt even relevant. did I just click the video for the sole reason of writing this one comment? why did i do that? what

  • @user-ty2ry2sk2w

    @user-ty2ry2sk2w

    4 жыл бұрын

    I knew that already but being reminded of it made me smile so here is a like from me

  • @jay-tbl

    @jay-tbl

    4 жыл бұрын

    @@user-ty2ry2sk2w Thanks

  • @balintbosnyak3383

    @balintbosnyak3383

    4 жыл бұрын

    And they hold hands in their sleep so they won't drift away from eachother

  • @human-1223

    @human-1223

    4 жыл бұрын

    I learn this from a manga

  • @nickf3242

    @nickf3242

    4 жыл бұрын

    This was news to me... Decided to take a stroll down the comment path and was enlightened by this tidbit of knowledge. I knew about the hand holding, but not this. I will probably be obsessing over this for the next few hours. It sparked a bit of curiosity and now I wanna know what happens if they misplace their beloved rock or someone takes it, do they freak out? I'm afraid of falling down a unplanned Google rabbit hole with this question. I'm not ready for the time investment at the moment. Thanks for the future Google query.

  • @heldersantos9928
    @heldersantos99284 жыл бұрын

    7:36 "impossible, it's like invade Russia in the winter". [Laughs in finish]

  • @aarneheikinheimo1256

    @aarneheikinheimo1256

    3 жыл бұрын

    I don't think Finland has ever invaded or even tried to invade Russia

  • @Inderastein
    @Inderastein3 жыл бұрын

    Rest In Peace Conway, Your Games Are Truly Fun Than Other Math Games

  • @jacekennedy2342
    @jacekennedy23423 жыл бұрын

    Why do I like that whiteboard desk so much

  • @ReezeZoronauto
    @ReezeZoronauto4 жыл бұрын

    Anyone else just recently been getting recommended videos mere minutes after they're posted

  • @coriae

    @coriae

    4 жыл бұрын

    the algorithm is tired of recommending the old catalog of at least 3 year old videos

  • @mikerphone.
    @mikerphone.4 жыл бұрын

    Rest in peace John. Your contributions to mathematics and mankind will be greater than you could've ever imagined.

  • @TheIndieGhost
    @TheIndieGhost3 жыл бұрын

    "get ready to social distance your heart out" me: that aged well then i see upload date me: oh

  • @shlimeball475
    @shlimeball4753 жыл бұрын

    I still have no idea what the golden ratio is even after watching dozens of videos on it

  • @sebdo2292
    @sebdo22924 жыл бұрын

    Me: Reads title Also me: Isn't that 𝘦𝘷𝘦𝘳𝘺 Vsauce2 game?

  • @trbld5219
    @trbld52194 жыл бұрын

    “Right?” Me:Yeah! “ *WRONG* !!”

  • @hallowizer440
    @hallowizer4403 жыл бұрын

    Promotions end at 1:39

  • @ordinaryshiba
    @ordinaryshiba3 жыл бұрын

    It's easy to see the number of soldiers needed if you know the number of moves and vice versa. Each move removes 1 chip and we need one final chip to stay on the high level so if n is the number of soldiers and m is the number of moves then n = m+1

  • @Savant_Ananya
    @Savant_Ananya4 жыл бұрын

    My guy really did get emotional at the end. I hope Covid-19 goes away asap

  • @carealoo744

    @carealoo744

    3 жыл бұрын

    I had to drop out of univeristy because its online

  • @prozior
    @prozior4 жыл бұрын

    Every time Kevin asks: Right? WRONG!

  • @seanjeremyhenrysihombing4066
    @seanjeremyhenrysihombing40663 жыл бұрын

    There is a solution to level 5....

  • @TheProGam3rHD
    @TheProGam3rHD3 жыл бұрын

    "The Game You Can't Win" Pursuit of Wonder

  • @jamesdowner
    @jamesdowner4 жыл бұрын

    RIP John Conway, and thank you Kevin for the tribute

  • @user-kx8pu6ys5i

    @user-kx8pu6ys5i

    4 жыл бұрын

    Yes

  • @Mauripsu
    @Mauripsu4 жыл бұрын

    "Is like trying to invade Russia in winter" BLITZKRIEG!

  • @bcn1gh7h4wk

    @bcn1gh7h4wk

    4 жыл бұрын

    "It's like trying to invade Russia, in winter, of 1025, BC, with horse chariots, and you're the stables boy."

  • @MrFram

    @MrFram

    4 жыл бұрын

    @@bcn1gh7h4wk laughs in Mongol

  • @Chrischi3TutorialLPs

    @Chrischi3TutorialLPs

    4 жыл бұрын

    Cause that worked out.

  • @oryionterrell6498
    @oryionterrell6498 Жыл бұрын

    Yooooo when he started talking about how to get to level 3 I paused the screen to look at the board and figure out how I would get to level 3 and 4 and I was almost spot-on That made me feel so smart lol

  • @coolphrogy9033
    @coolphrogy90333 жыл бұрын

    This man is CEO of “Right? WRONG!”

  • @einfachflo1365
    @einfachflo13654 жыл бұрын

    7:37 Right in my Gefühl.