Brilliant: https://brilliant.org/vsauce2

Thanks to Brilliant for sponsoring this episode.

*** SOURCES LINKS AND MORE ***

โThe Ways of Paradox and Other Essaysโ by Willard Van Orman Quine: https://www.amazon.com/Ways-Paradox-Other-Essays-Revised/dp/0674948378/

Zeno of Elea, Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/zeno-elea/

Zenoโs Paradoxes, Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/paradox-zeno/

Convergent Series, Khan Academy: https://www.khanacademy.org/math/calculus-home/series-calc/seq-conv-diverg-calc/v/convergent-and-divergent-sequences

โGame Show Problemโ by Marilyn vos Savant, Parade Magazine, 1990: http://marilynvossavant.com/game-show-problem/

โSolution to the Grandfather Paradoxโ by minutephysics: https://youtu.be/XayNKY944lY

โThe Faint Young Sun Paradox!โ by MinuteEarth: https://youtu.be/qbnaes8X4iQ

***********************************

Vsauce Links

Website: http://www.Vsauce.com

Twitter: https://twitter.com/VsauceTwo

Facebook: https://www.facebook.com/VsauceTwo

Hosted, Produced, Writing Contributions And Edited by Kevin Lieber

Instagram: http://instagram.com/kevlieber

Twitter: https://twitter.com/kevleeb

Website: http://kevinlieber.com

Research And Writing Contributions by Matthew Tabor

https://twitter.com/matthewktabor

Writing Contributions by Michael Stevens

https://youtube.com/Vsauce

VFX By Eric Langlay

https://www.youtube.com/c/ericlanglay

Special Thanks Paula Lieber

https://www.etsy.com/shop/Craftality

Select Music By Jake Chudnow: http://www.youtube.com/user/JakeChudnow

Thanks to Brilliant for sponsoring this episode.

*** SOURCES LINKS AND MORE ***

โThe Ways of Paradox and Other Essaysโ by Willard Van Orman Quine: https://www.amazon.com/Ways-Paradox-Other-Essays-Revised/dp/0674948378/

Zeno of Elea, Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/zeno-elea/

Zenoโs Paradoxes, Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/paradox-zeno/

Convergent Series, Khan Academy: https://www.khanacademy.org/math/calculus-home/series-calc/seq-conv-diverg-calc/v/convergent-and-divergent-sequences

โGame Show Problemโ by Marilyn vos Savant, Parade Magazine, 1990: http://marilynvossavant.com/game-show-problem/

โSolution to the Grandfather Paradoxโ by minutephysics: https://youtu.be/XayNKY944lY

โThe Faint Young Sun Paradox!โ by MinuteEarth: https://youtu.be/qbnaes8X4iQ

***********************************

Vsauce Links

Website: http://www.Vsauce.com

Twitter: https://twitter.com/VsauceTwo

Facebook: https://www.facebook.com/VsauceTwo

Hosted, Produced, Writing Contributions And Edited by Kevin Lieber

Instagram: http://instagram.com/kevlieber

Twitter: https://twitter.com/kevleeb

Website: http://kevinlieber.com

Research And Writing Contributions by Matthew Tabor

https://twitter.com/matthewktabor

Writing Contributions by Michael Stevens

https://youtube.com/Vsauce

VFX By Eric Langlay

https://www.youtube.com/c/ericlanglay

Special Thanks Paula Lieber

https://www.etsy.com/shop/Craftality

Select Music By Jake Chudnow: http://www.youtube.com/user/JakeChudnow

Uploaded: 2018-04-24 18:23:06

Number of Views: 836,028

Number of Likes: 35,808

Category: Education

Caption: Vsauce kevin here and you have a dilemma. i have two envelopes and you can only . choose one. there's door number one and there's door . number two. oh there's actually three envelopes here . oh great now we no longer have a dilemma . here's why dye comes from the greek . twice and lemma means premise so a dye . lemma involves two premises from which . you have to choose adding a third . envelope means that this choice isn't . technically a dilemma but it does set up . a very famous paradox wait . let's dissect the word paradox like we. just did with dilemma to find out . exactly what a paradox is okay para . comes from the latin distinct from and . dox comes from doxa meaning our opinion . paradox translates literally as distinct . from our opinion so there you go now . distinct from our opinion that didn't . really help at all i thought a paradox . was like an unsolvable brain teaser so . how do three envelopes set up a paradox . what is a paradox . [music]. in 1961 logician and philosopher willard . van orman quine outlined two the three . categories of paradoxes and i have them . each hidden inside these three envelopes . one represents the kind of paradox that . you're most familiar with those that . defy logic like the impossible waterfall . from this video's intro the other two . are what. well let's crack one of them open and . find out false cynical this is why . achilles can never catch a tortoise will . use this bootleg rambo to represent . achilles and a ninja turtle pez will be . our tortoise if the tortoise gets a 100 . meter head start then achilles starts. running by the time he gets to the 100 . meter mark the tortoise will have moved . a another meter it takes achilles some . more time to get to that 101 meter mark . and in that time the tortoise has moved . even further achilles will always be . catching up to the place where the. tortoise was as the tortoise inches . forward the gap gets smaller and smaller . but the tortoise is always slightly . ahead. according to greek philosopher zeno of . elea who dreamed up this paradox 2500 . years ago the fastest runner in the . world can never overtake a tortoise in a . race because you can infinitely divide . the distance between them as the . tortoise advances but that's ridiculous . we know it's not true even with a head . start i could outrun a tortoise and i'm . no achilles so how can this be a paradox . zeno knew achilles could catch up to the . tortoise in real life but he couldn't. prove it mathematically he thought there . would be an infinite number of new . points for the tortoise to reach that . achilles had to reach because he didn't . know that an infinite series of numbers . could add up to a finite value no one . knew that. for another 2,000 years what we now call . a convergent series 1/2 plus 1/4 plus . 1/8 plus 1/16 plus 1/32 goes on forever . but it eventually adds up to 1 and at . that one is where mathematically. achilles finally reaches the tortoise we . knew that achilles could catch up to the . tortoise but it took inventing calculus . for us to prove why which is why this . paradox that confounded great minds for . thousands of years is false itical . described by quine like this a false . cynical paradox packs a surprise but it . is seen as a false alarm . when we solve the underlying fallacy. okay that's one paradox envelope down . and two to go and behind number two we . have veridical for this we need a game . show okay i'm gonna replace the two . envelopes we've already opened with some . prizes how about 1 million dollars will . go into one of them and the glob glow . gab collab will go in the other good . enough prizes any the third envelope . still contains the term for the final . type of paradox which we'll get to later. all right i will shuffle these up so you . don't know which is which now you've got . three envelopes x y & z pick the correct . one and you win the grand prize after . you make your selection let's say . envelope x the game show host reveals . what's inside one of the two remaining . envelopes. it's the glob. now there are only two envelopes left . the one that you chose and the remaining . mystery envelope it gives you the option . to switch your envelope should you do it . does it even matter i mean at this point . your odds of winning are just 50/50 . right no you should always switch and . here's why the odds of winning with your . first chosen envelope are 1 in 3 so you . have a 33. 33% of being wrong when the . game show host revealed the glob it . didn't suddenly improve your odds to . 50/50 the proof is in the options after . first choosing an envelope the thing . revealed by the host will never be the. money because well that would ruin the . tension of the gameshow so if your . initial 1 out of 3 pick wasn't the money . and the money is why and the host will . reveal z if you chose wrong and the . money is z the host reveals why if you . luckily chose the money the first time . then the host can reveal either a z or y . it doesn't matter no matter what you're . still stuck in that initial 33% chance . that you chose right the very first time . but if you switch regardless of the . prize revealed you now leap into the 66% . zone you've doubled your chances of . getting the money to put it another way . when you're asked if you want to switch . you're actually being given a dilemma do . you want to keep your single envelope or . do you want both of the other two it . just so happens that you already know . what's inside one of them but since the . one revealed will never contain the. money the chances that the other . unopened one has the money are twice as . high . as the first one that you chose the . monty hall problem blew up after a 1990 . parade magazine columnist advocated . switching doors in the same scenario. from the game show let's make a deal . when she told readers they should always . switch to improve their odds of winning . nearly a thousand people with phds wrote . in to tell her that she was wrong she . wasn't wrong they were so the monty hall . paradox like the potato paradox we . recently covered is an example of one . that is a veridical . paradox one that initially seems wrong . but is proven to be true coin said a . veridical paradox packs a surprise the . surprise quickly dissipates itself as we . ponder the proof okay there are . paradoxes that seem absurd but have a . perfectly good explanation and ones that . could seem false and actually are false. because of an underlying fallacy even if . it takes a major advance in math to . prove it. this last envelope contains the kind . that we think of when we all think of . paradoxes and tena me the grandfather . paradox where you go back in time to . kill your grandfather when he was a . child but that means your father was . never born so you were never born so how . can you go back in time to kill your . grandfather mini physics proposed a . solution to this but these types of . paradoxes are not true or false . actually they can't be true and they . can't be false . as quoted they create a crisis in . thought i am . lying if i'm lying when i say that then . i must actually be telling the truth but . how can i be telling the truth . if i'm lying the liars paradox is an. example of antinomy which literally. means against laws and highlights a. serious logical incompatibility quine . said klein said that this tape thing was . a good idea in theory but in practice . not so much coin said and antinomy packs . a surprise that can be accommodated by . nothing less than a repudiation of part . of our conceptual heritage here's the . thing antinomies are paradoxes to us all . false itical and veridical paradoxes are . only paradoxes to those who don't know . the solution but they still have value . every time we resolve a scenario that . runs counter to our or someone else's . initial expectations every time we learn . the how and the why and share that . information we're refining and . clarifying knowledge which makes all. three types of paradoxes excellent tools . for reasoning whether or not something . is paradoxical to an individual depends . on the accuracy of their expectations . today modern mathematics has given us . the ability to show that zeno's . paradoxes are false cynical but they. were pure antinomy unresolved to. everyone for millennia coyne himself . said one man's antinomy is another man's . false cynical paradox give or take a . couple of thousand years who knows which . antinomies of today will be solved in . the future right now we struggle with . the paradox of the faint young sun our . current knowledge of stars says . billions of years ago our sun wasn't hot . enough to keep the earth from being a . all of ice but our geological evidence . shows an ancient earth with liquid. oceans and budding life when everything . should have been frozen how could the . earth have liquid water without a sun. hot enough to melt ice its antinomy . until we fully comprehend the situation . maybe our current understanding of the . sun isn't perfect or maybe our knowledge . of early earth is missing some pieces . a paradox is a problem where the . solution is or is made to seem. impossible sometimes they're . purposefully designed for fun because . our minds like puzzles sometimes we just . stumble on a gap between what we know . and how we talk about what we know and . what is actually true when we solve an . impossible antinomy it becomes false. itical or veridical someone who knows . the answer can see what the problem was . all along we tricked ourselves by. knowing too little or by asking the . wrong question in one way or another all . paradoxes come from people by. challenging us to find the flaw or fill . the gap in our knowledge paradoxes help . us define and push our intellectual. boundaries there's always more for us to . know whether we know it or not and as . always thanks for watching . hey if you want to play the monty hall . game yourself you can do that right now . over at brilliant but the best part . about it and why i'm happy to work with . them is that brilliant helps you learn . and refine your own knowledge so after . you work through the initial problem you . can take it to the next level with . variants that make sure you really . understand what's happening so to . support vsauce2 and your brain go to . brilliant orange slash vsauce2 and sign . up for free the first 500 people that . click that link will get 20% off the . annual premium subscription which is an . excellent deal for everyone . [music]. .