The Futurama Theorem
2015 ж. 28 Сәу.
1 302 633 Рет қаралды
The Futurama episode The Prisoner of Benda features a machine that allows two people to switch minds. The problem is that two bodies can only switch minds once. Fry and Co. goes wild on the mind switching machine and have to resort to some serious math to get back into their own bodies. Our mission in this video is to give a crystal clear explanation of the Futurama theorem.
As an added bonus there is also some Stargate mind switching action towards the end of the video.
(added 15 August 2015) We just posted a follow up video: • The parity of permutat...
Enjoy :)
I love how Farnsworth looks skeletal when he pulls his shirt up, yet has a paunch when his shirt is down.
When you put your arms up your belly disspaears a little bit as well
lol
i like when that hapens in other shows aswell like in adventure time, the ice king look plump but is really skinny.
@@bensiniawski8719 his weight actually fluctuates but he's usually depicted as skinny. It works better for the snapping sound effect the use when he moves his arms
Schrödinger's Gut
I love how he names everyone involved except for Zoidberg. He's a true fan.
+Jerrad Willis Yes, I am a real fan :)
But what about Zoidberg?
What an honor
14:15
Why not zoidberg?
"They bring in help from some mathematicians. It's actually the Harlem Globe Trotters of the future, that turn out to be excellent mathematicians, apart from being excellent basketball players" Futurama is such a great show that that statement make sense.
One of the greatest shows ever :)
I'm glad someone said it thank you
Fun fact; this strategy is used to memorize and solve Rubik’s cubes blindfolded
yes, i know. At the end, you just remember about 20 letters and go doing T perm or modified Y perm again and again and again.
@@alesmasarik4578with the occasional R perm depending on if the number of letters you memorised was odd or even
Futurama had one of the most mathematically literate writing staffs on television. Co-creator David X. Cohen holds a BA in Physics from Harvard and a Masters in Computer Science from Cal-Berkeley.
Damn, that's one qualified comedy writer.
@@67tedward a surprising amount of people in entertainment are
Yeah this show is beyond calculus and for an actual math major.
Everyone should be so well educated. Then we wouldn’t have so many problems 🤣 and have more good comedy shows like Futurama with funny science jokes.
didn't the combined creative/writing staff on this show hold like 3 PhDs and 10+ Masters degrees
I love how casually he drifts between discussing serious math to "haha we also have the robot king in this episode"
tommy karrick emperor
"Apart from that, it's just the usual crowd: the professor, and Leela, and Hermes... all these guys." I know you didn't mention everyone, but I got a chuckle out of how you ignored Zoidberg.
Everybody forgets about Zoidberg ... :)
oh my god
Lol it's very fitting then.
Isaac Banta zoidberg is boring
But what about fry
I love how it shows the globetrotters are true mathematicians in that they didn’t stop at just finding out the single solution to their particular mess, they wrote a method that is true for all possible permutations
I've always admired the fact that the creators of futurama invented a sound mathematical theorem for that episode but I was never able to understand how it worked so thank you very very much!
Stargate SG-1 did it first.
@@unclecreepy7025 Stargate solved a simpler special case of the problem.
They themselves have stated they were easily the most over educated writing staff for a tv show
@@doomedbringer this is true, have you ever looked at the amount of crazy big school grads and phd's were on that writing team?
Dude kinda looks like a younger Farnsworth
I was thinking the same thing when the professors picture was up right next to him
well...he definitely is bald and wears glasses
OMG can't be unseen
Wow lol.
only a little younger, he he he
Whats funny about how zoidberg and fry are in their own separate cycle is that it implies they just hopped on the machine and switched minds for fun because everyone else was switching minds trying to sort themselves back again. They probably didn't understand what was happening and just wanted to be part of the action which is hilarious because it fits their characters so well.
this futurama episode was one of the very few times that i was able to put my group theory knowledge to use. my math degree was totally worth it because of this.
Yes, great episode and nice math. Really have to do some more videos featuring all those other amazing bits of mathematics that are hiding in Futurama :)
"can I change my mind?" "let's find out!"
Easy.. make sure the last two are robots, then switch their memory unit. xD
Bucket doesn't matter too
Of course the bucket matters! It has a romantic relationship with Scruffy.
Maybe their memory units don’t fit.
@@TotoDG uhh then make sure the last 2 have matching slots.
They’re not the ones who built the robots. They have no control over that.
Its amazing how this theorem is so much similar to how we solve a rubik's cube blindfolded ! In the scrambled rubik's cube we just declare a single piece as the "buffer" and make these cycles to eventually sort out all the pieces !!
I have used this when programming and holding information in temporary variables it's very useful for us computer scientists
FisforFenton Yep, same idea :)
Though to be fair it appears much more rarely you can't directly use the third temporary storage space again and again
That actually makes tons of sense and is a very practical use of this therom!
@@feritperliare2890 what would be an example of a situation like that? I've never encountered one, not that I can think of at least.
@@iwikal Maybe if you wanted to swap temporary variables, so you would have to bring new variables into the mix in order to hold the values of the old ones. Would be important in environments where you have to do it in the most efficient way possible
A lesser show than Futurama would figure that it's full of soft science played for laughs anyway, and thus doesn't need to care about being correct about any of it. It's really nice that they didn't go with that line of thinking.
I hate the "if it looks complex enough, why does if matter) approach.
@@wariolandgoldpiramid yeah me too.
I love how mathematical Futurama is. In one episode they reference Flatland, fractals, 4D, and Mobius strips all at the same time! My second favorite line in the show, after "I'm afraid we're going to have to use MATH" is this: Amy: "There's one more lap to go!" Thug: "No, they're still on the same side. It's a Mobius strip remember?" Zoidberg: "You kids and your topology!" Hahaha I'd put that on a shirt. Topology
Mandelbrot Set We'll probably do a couple more videos on all the math in Futurama. So much good stuff.
Amusing because you can think of it as a lap of infinite length.
Once around both same sides of the half twist, and back to the start and finish line!
When television actually knows what they are talking about
what episode was it that had those things?
Even Mathologer forgets Zoidberg lol
Steve Bermeo Poor Zoidberg :)
+Community College Genius Did you actually watch the video?
@Kinsey Swartz You should be asking your self this, Community College Genius was not talking about this video for you to be talking like that. Makes you look slow on comments. And KZhead changed, it's no longer + when we comment to another's comment. KZhead needs to make up their mind they keep changing things.
@@ZekePolarisBSH alright there bud no need to start ww3 over it :P makes you look slow over something so trivial... just to give you a dose of your own medicine @(^_^)@
@@RajSingh-qc6lq whoa chill out child ww3 already started and it wasn't me. You don't even know what medicine is.
I don't know if someone noticed this already, but in stargate they're just applying th efuturama theorem without actual knowledge of it: they have 2 2-cycles, so each couple is working as the futurama theorem's {x,y} for the other couple.
Except that Stargate episode came out 11 years before this Futurama episode. Although they do time travel, so I suppose O’Neil could have watched Futurama in the future, being a Simpsons fan and all.
So in other words: Stargate did it first but because it was the only real applicable use of math and science (fiction) in Futurama, everyone took note.
I'm glad I'm not the only one that immediately thought of Stargate.
Good news everyone! I've invented a device which makes you read this in your head, in my voice!
Damnit you got me
I read this in Morgan Freeman's voice
lol it worked
XD holy shit
culwin.
My favorite was some kind of race it ended up as a quantum finish, the prof. says "you changed the outcome by observing it!" lol
If I had a penny for every time there was a one-way mind switcher in a science fiction series that had to be untangled using math, I'd have two pennies, which isn't a lot but it's weird that it happened twice.
Wait who else did it
@@baaccaab2622 It's in the video.
My favorite animated series. There's always that math reference that I laugh at alone when watching with friends.
Kajidimeh92 Maybe also check out the follow-up video that we published earlier today. Also, there is another video in the pipeline that is about different bits of amazing math in Futurama :)
No fair! You altered the outcome by trying to measure it!
"And they say pure math has no real-world applications!" I was totally expecting this quote at the end. Thanks for explaining this theorem, in the episode it happens so quickly I didn't know what was going on.
... and then I learned about Mind-switching mathematics. KZhead is wonderful.
The solution that I came up with when I first saw the episode: -Make 2 robots for mind storage -Do the mind switching till the robots are left with each others minds -Kill them
Grime's corollary, first presented in a video he posted here on KZhead, shows that the procedure used in the Futurama episode is sub-optimal. You see, since Fry and Zoidberg had only swapped with each other, they could take the place of the basketball players, and the whole mess could have been sorted out in four fewer moves.
I really want to see someone solve preexisting problem by citing this theorem/lemma/fact.
Wash bucket has always loved you.
I'm glad, that no numbers were harmed in the production of this video :)
It was such a clever episode. One of my favourites.
Check out Stargate SG1 S02E18 Holiday. Literally same idea except it came out before Futurama was on TV.
@@emersonsnyder369 He mentioned it
futurama, stargate and Math. serotonin overload! well explained. thanks.
I love how you make math relatable both to myself and my kid at the same time!
+atom - Yoga & Feldenkrais That's great :)
Great lecture. Thank you. My first encounter with a mind switcher was the Red Dwarf episode Bodyswap. This was also a good series when it came to playing around with theories and theorems.
Lewis Fitzjohn Ah, yes, totally forgot about that one. Red Dwarf, one of my all-time favourite series. Have to rewatch this episode now to remind myself what exactly happened there. Thank you very much for this bit of information :)
I saw a film yesterday, that reminded me of this video. It's called Self/less . It's about a super rich old man who uses a mind swapping machine to live in a younger guy's body after his death. Not to spoil too much, I'll just say that the machine gets used quite a lot in the film and I found it quite interesting. It's directed by Tarsem Singh who also gave us 'The Fall' and 'The Cell'.They're all pretty good films.
@@lewisfitzjohn Kinda sounds slightly similar to the movie Freejack
@@Eidolon1andOnly Wow this looks awesome. Thanks for the recommendation. I'm gonna watch this.
Finally proper recognition futurama deserves.
lol "We'll have to use math."
Yup, they definitely scienced the shit out of it...
This is why Futurama is one of my favorite shows.
awe poor Zoidburg, always getting forgotten about. But the maths and cosmology and physics involved in the Futurama show is one of the greatest reasons that I love the show. Even the time machine and fry moving through time is set up pretty nicely. The episode where we find out about Bender as a youth and this one are my two favs.
Thanks for this video Burkard - I watched it for the first time a few weeks ago and found today I needed to use a variation of the Futurama Theorem to update some database records I thought about in the manner presented here and it became simple.
Futurama is so brilliant, definitely one of the best tv shows of all time.
Bringing identical twins as a spare bodies would save one move ;)
Mateusz Szczepara no cerebal immune responce because same antigens lol
Bender and Flexo
With him talking about “messes” I like to think of him sitting his kids down and giving this exact lecture in reference to cleaning their rooms.
Thank you so much for explaining this! I always loved this episode but never understood the ending scene, now it makes sense. This is so interesting!
I think if somebody mind-switched me, and tried to pretend to be me, that my family would know instantly. Everything I do is so awkward, I think it'd be hard to authentically copy my mannerisms! And honestly, I think that's true of everyone. When you see a familiar person in the distance you can usually recognize them just by how they move. I think body movement is almost as unique as a fingerprint.
The pattern of the pressure that you make in the ground with your feet when you walk was actually comproved to be more unique in each person than fingerprints
Ever since watching that episode ive watched to sit and work this out to see if they got it right. Thank you for doing it for me lol
It's kinda funny that in almost every mind switching scenario in movies and cartoons the characters' voices change to match their minds :) Inb4: yes, I know that this is for the viewers to be able to track who's in whose body, but it's still funny ;)
You have a nice, calm voice and make the confusing mathematical jargon easy to follow. Great video!
“I’m afraid we’ll have to use.. MATH.” Damnit do I have to take my meds today?
i had this same problem once
All I could think of was that Stargate SG-1 episode. I'm really glad you brought it up.
this channel has caused me think about math much more during the day. I truly appreciate your work. I wish I could make sence of the formula that they had on the board though. I grasp the concept when I see it done physically but the formula still looks like Greek. again though, I am greatful for your content
Should have started this video with a "good news!"
Mathematicians: "So this is how you sort out this mess." Me, a philosopher: "...but what are the ontological implications of mind-body dualism??"
What are you smoking? The mind is not independent of the brain. Even assuming that you could, somehow, copy/paste all of the neural patterns the brain would still be subject to the other factors of the physical condition of the new body. Ontology is a philosophical school of thought that offers nothing and means nothing. The "ramifications" of dualism being true would be beyond the pointless realm of ontology and would actually have implications in biology, neurology, and you know, science.
@@Xeroisawesome First of all, ontology isn't a "school" but a _discipline_ of philosophy, dumbass. And oh yes, how could I forget that this would have implications "in" (sic!) biology, neurology, *and* (!!!) science - because in your mind, biology and neurology apparently aren't science for some weird reason. Would you mind telling us what exactly these implications of mind-body-dualism (!) for biology, neurology, and (!!!) science are without any reference to ontology? Do you even know _what_ ontology is? Aside from a "school" of philosophy, of course, lol. All of that aside though, I'm not actually a dualist. If you had any context awareness, you would have realized that what I meant was: what are the philosophical ramifications of mind-body dualism being true _within the narrative of Futurama?_ - which it pretty much has to be if bodyswap devices can exist in that story.
@@tarvoc746 ya fuckin' killed em' dude
Yes... I'm happy that there are people that think about these kinds of questions! ^^ Tell me when you found an answer! ;) What's for dinner?
@@jackmclane1826 my point was that actual sciences, like biology and neurology, would be affected if there was proof of a mind outside of our current understanding of neurochemistry. I specifically listed those two sciences and then remarked on science in general in order to separate science from philosophy. My phrasing could have certainly been better and would have communicated my point more if I had paid more attention, so that particular miscommunication is certainly on me. So let me be one hundred percent unambiguous on my next point. Philosophy, in virtually every form, is completely and utterly useless. All philosophy boils down to, however you try to swing it, is "I think this." There is no objectivity, no tests, nothing but thought experiments that demonstrate nothing and serve no useful purpose. Is the ship of Theseus a new ship, or the old ship? It doesn't fucking matter, it will never matter, and it holds zero relevance. Disciplined or not, philosophy is a complete waste of time, other than for the purposes of mental masturbation. At least when I get done jerking off, though, I have a little something to show for it.
I can't even watch this episode sometimes lol. I end up pausing it and try to figure out a solution. Glad I found this video!
Thanks for massively over explaining something explained easily within the episode
Wonderful! I'm loving your channel! To me, math is the ultimate logic game. When I heard your rule around 2:30 ("once two bodies sit on the chair, they can't sit there again"), I was a bit confused with your phrasing: did you mean a body can't sit more than once, or just the PAIRING can't sit more than once. Indeed, as I kept watching, you meant the pairing.
Glad you like the videos and, yes, I meant the pairing.
This is one of two reasons Futurama is the greatest animated show of all time. The other is it‘s portrayal of the future...
But Konosuba
I saw this in the recommended, I really like this guy. Solid stuff so I subbed!
Who else is watching this in 3020? Thanks alot for the help, this really saved the day, thank god for this channel or me and my friends would have been srewed
Check out part 2 (if you dare :) kzhead.info/sun/qpSmqMinbKeoknk/bejne.html
i luv you man. wow ur my new favorite subscribe. i always new i liked that episode, and unfortunately i figured out the little math problem right away, so i saw it as a super funny joke. i like how you explain this, hopefully more people can appreciate this show. anyways, like ur show.
just turned 33. computer Science major. but always have been in sales and business. scince is my passion, research, etc. how do i start about getting into a good field with minimal experience, but great understanding and ability to learn?
Ace Mcloud Well, you could always go back to college and do another degree (I've never really left university and I am still having a great time). Or you could work your way through some of the excellent free online courses, for example, the ones offered my MIT. I guess the main thing it to have the time and resources to really be able to go for this in this respect :)
Ace Mcloud Glad you like what we are doing and thank you very much for saying so :)
+Mathologer are you saying I can clean my room using this method?
When you want to become a mathematician but your mom tells you to be a cartoon producer
I love you so much for your captions!!!
I love both those shows :) great explanation of the theorem as well, good work.
Dave Foster Glad you like what we are doing and thank you very much for saying so.
This is what you get when the writers of the show have over 50 combined years of Harvard schooling. This show is brilliant
14:10 That was the first solution i thought of! Awesome!
SomeGuy named GROM Cool.
I’ve been waiting for a video explaining this for a long time
I'm really enjoying your clips. Great fun and very well presented.
Richard Man Glad you like what we are doing and thank you very much for saying so :)
This is actually how you solve a Rubik's Cube ~,..,~
mvpmickey1 Yep, definitely very similar :)
Oooohhhhh, you just _switch minds_ with your Rubik's Cube and have _it_ do all the work! _That's_ where I went wrong!
What's a rubik?
genius at mathematics, cant recognize a troll
@@skylermagnificent5422 A human _can't_ switch minds with a mindless, inanimate piece of plastic?! Ohhh, _if only_ I'd known that _before;_ I could've made a funny _joke_ instead of just embarrassing myself in front of the whole Internet!
4:40 Even you forget about Zoidberg; poor Zoidberg
+Marcos Carballal Poor Zoidberg :)
The most recent time I rewatched this episode I paused and tried to understand the theorem on the blackboard (holoboard?) and didn't have much luck. I had another go after watching this video and it's wonderful circular shifting animation and I think I get it! I notice that the maneuver following the critical point with the exclamation mark wasn't addressed on the blackboard, I think that part is a nice addition from our Mathologer! The blackboard theorem doesn't need this to be a solution, though; the way I understood it was that after you have cleaned up one cycle the globetrotters will have been switched, but you can still go ahead and resolve the other cycles and save their switch for when the whole mess is sorted out. Come to think of it if there was an even number of cycles they wouldn't need a switch...
I didnt know math could be so interesting, fantastic job!
he looks just like doctor farnsworth
+Greg Cook Good news everyone!
professor*
OooOoh mmyyyyyy
Fuckin' math, man.In all seriousness though, what you do is amazing!I wish they tought math like this in my schooling days.
Futurama theorem? Years before this episode of Futurama, I remember the exact same plot happened in an episode of Stargate. They discovered a mind switching machine that had the same restriction preventing it to switch the minds back between the same bodies. Love both shows BTW. Edit: WoW, you have mentioned the Stargate episode. I am surprised anyone knows about Stargate these days.
I watched all Stargate episodes :)
Thank you for the video, it's very interesting and transparent.I think this episode is cool, because instead of using new machine, they used math that sorted out the mess.
This problem and solution have a very “Olympiad” flavor
The ultimate joke is the wash bucket is a literal +1 which invalidates the entire thing since it doesn't really need to be returned, breaking the entire formula.
Yeah but that would result in someone being stuck as a wash bucket
The alien writing at the top of the screen at the beginning says "No numbers were harmed in the production of this video"
Thanks for bringing up Stargate, I love the mind switch episode
what's weird is according to this guy, the Tick episode came out 3 years before the Stargate episode, but the old guy in the Tick episode looks just like Machello in the the Stargate episode. Did Stargate imitate the Tick episode?
The Tick did have a pretty solid cult following (and it should, it's hilarious - like Freakazoid) so it wouldn't surprise me.
He forgot The Prisoner episode Do Not Forsake Me Oh My Darling
I find it really interesting that I do this when pairing the edges of the rubik's 4x4x4.
Damn. A great watch. And an awesome show. Sad that it's gone.
Here is my graph theory + geometry solution. Arrange each cycle into a regular polygon. Now, use the first new person to reflect each vertex in the polygon to a new vertex in the polygon. Use the second new person to reflect over a different line. Recall that the reflections around two distinct lines is a rotation. Thus, we can choose our two lines in such a way that each vertex rotates to the vertex to their immediate right. This gives everyone to be back to their original bodies.
I wish public education was like this.
Swap kid's brains and make them do maths or be forever stuck in the wrong bodies.
+Katzen4u He means to watch videos and explain them
+Katzen4u xD amazing idea
I'm with Katzen
Make a second set of chairs
stellvia hoenheim Actually, it's that the same bodies can't transfer minds twice, but that's essentially the same problem.
Really good video, didn't expect the mini-history of mind switching on television, I thought it was a nice touch. I would of enjoyed if you could of wrote down pieces of the theorem, as we worked through the explanation, ending with a complete theorem, including various steps, and formulas. I came out with understanding how to solve the crisis, but not an understanding of the math behind the theorem.
besides the content, your videos deliver a superb production quality.
i grew up on stargate.
Robert moon Same here.
Robert moon I was just about to say that.
I grew up on Earth.
I looked at the board in the episode and thought it was all bullcrap math XD
+Jonathan Mounce No, it's the real thing :)
That was in a recurring thing in Futurama, if I remember correctly. They liked to put real math references and jokes within the show.
You should know better than that! :)
same i though it was random numbers and they didn't meant anything at all
When a show or movie uses math like this, it has to be true or they get yelled at by everyone.
This was pretty fun to think through, I took the puzzle after the first two switches and added on more person to solve the problem before it got out of hand. I used Fry in this case, Fry trades with Doctor, Amy trades with Fry, Doc with Bender, and then Fry trades with Bender. This makes me think of many visual puzzles in video games or even the rubik's cube where being so close to a solution doesn't work and really makes for far more steps later. You sort of have to "break" the problem even more in order to fix it. Adding one person doesn't help because as soon as you see the way to solve on person's out of body experience, the other two are stuck. As you point out in this case it is Amy and Bender. I sort of thought through what my win condition was, my idea being "putting Fry in Bender's body and Bender in Fry's body and the other two correct before I switch Fry and Bender." That way I eliminated the action I can't take and worked to solve this slightly simpler problem. Bender traded with Amy, so to get Fry into Bender's body without trading with him directly (and keep my win condition by saving that trade for last) he has to get there from the Doctor. Then I fix Amy, then I fix the Doctor, and then I have my win condition and one swap later it's solved. I literally have to have everyone in the wrong body in order to get them in the right body. It helped that the first trade I did was symmetrical of the last one, with both original bodies having swapped twice and the new helpers having swapped once.
Stargate and Futurama excellent , now i have to rewatch those awesome shows
and yet I din"t get the royal crown. GODDAMN IT !
It’s happened. I’ve reached the end of the internet.
I love the way that you say you “really, really “and “very, very “
I want to give you dozens of likes for putting Stargate in the video. Stargate is my childhood. Thank you.
If you like your mind switching with less maths and more laughs, then may I recommend the episode Bodyswap from the BBC comedy series Red Dwarf? (The funniest thing to happen to science fiction since Yoda pretended to be a leprechaun for St. Patrick's day!)
Red Guy and Blue Guy? Ethan "Bubblegum" Tate and "Sweet" Clyde Dixon think that's jive!
+Anon archist Just trying to be as understandable as possible even to people who are not hardcore Futurama fans :)
This series is great. I wish I had you for all my past math classes. I am not a slouch at math, mind you, but in watching your videos I have learned some things I never knew and have a clearer understanding of some things I thought I already knew. Please keep up the good work and come lecture at University of Michigan or Oakland University some time! If you have a chance do a Wile's proof of Fermat's last theorem so that Homer could understand it.
+ctbram0627 I think a for dummies version of Wiles's proof is really beyond me/impossible. Having said that I've been thinking about how one could explain Fermat's proof that x^4+y^4=z^4 does not have any (non-trivial) solutions in integers to Homer. Still pretty tricky but I think something I can do nicely in 15 minutes :)
I saw and loved a few Mathologer videos so I'm going through them in order from oldest to newest, very interesting-