An Infinity Paradox - How Many Balls Are In The Vase?
ฝัง
- เผยแพร่เมื่อ 7 มี.ค. 2021
- Watch over 2,400 documentaries for free for 30 days AND get a free Nebula account by signing up at curiositystream.com/upandatom and using the code "upandatom". Once you sign up you'll get an email about Nebula. If you don't get one, contact the curiosity stream support team and they will set you up with a free Nebula account right away.
Nebula: watchnebula.com/
The Ross-Littlewood Paradox
Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
/ upandatom
Visit the Up and Atom store
store.nebula.app/collections/...
Subscribe to Up and Atom for physics, math and computer science videos!
/ upandatom
Follow me @upndatom
Up and Atom on Twitter: upndatom?lang=en
Up and Atom on Instagram: / upndatom
A big thank you to my AMAZING PATRONS!
Brian Wilkins, Michael Seydel, Cy 'kkm' K'Nelson, Thorsten Auth, Purple Penguin, Gary Leo Welz, Dr. Varun Pant, James Palermo, Berj Bannayan, Chris Flynn, Jeffrey Smith, Jessica Rose, David Johnston, Rick DeWitt, Yana Chernobilsky, Lynn Shackelford, Adam Thornton, Andrew Pann, Anne Tan, Thomas Krause, Brian Kent, Robert Hillier, Aaron Moffatt, Alex Hackman, Thomas V Lohmeier, Joel Becane, eris esoteric, Artem G., Michael Hunter, Aaron Dorn, Paul Barclay, Austin Rose, 12tone, Zhong Cheng Wang, Corey Sampson, Damien Holloway, Mikely Whiplash, John Lakeman, Jana Christine Saout, George Fletcher, Michael Dean, Chris Amaris, Matt G, Broos Nemanic, Dag-Erling Smørgrav, John Shioli, KhAnubis, Joe Court, Todd Loreman, Susan Jones, Dario, Håkon J. D. Johnsen, Will Miller, Dagmawi Elehu, Philip Swan, Hansjuerg Widmer, Scott Lemen, Carlos Gonzalez,
Gabe Roche, Jonathan Ansell, Arsalan Noorafkan, Thomas Kägi, Courtney Rosenthal, Dominic Riverso, Joshua Adams, Jeroen Melchiors, Andrej Zon, Richard, Chris Teubert, Dylan Kolstad, Fran, Joe, Chester Stadler, John Sokolowski, Robert J Frey, Martin Zenuik, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Christopher Phipps, Louis M, ROBERT C PAYNE, kadhonn, Moose Thompson, Hal Roseman, Andrew, Tamara McDermott, Charles from USA, John Klinkner, Hassan Sedaghat,
Rob Napier, Sam Ross, Peter Walsh, Osa and Beth Fitch, Garrett Chomka, Jeff Schwarz, Somebody, Josh B, Jimotei, Zach Tinawi, Bobby Butler, Rebecca Lashua, Pat Gunn, Luc Ritchie, Elze Kool, RobF, Aditya Anantharaman, Frédéric Junod, Vincent Seguin, Bernard Wei, Help I'm trapped in a driver's license factory Roberts, Shawn, Ken Takahashi, Jesse Clark, Steven Wheeler, The Doom Merchant, Philip Freeman, Jareth Arnold, Simon Barker, Simon Tobar, Dennis Haupt, Ginny Liz, Lou, amcnea,
Renato Pereira, Simon Dargaville and Magesh.
For a one time donation, head over to my PayPal :) www.paypal.me/upandatomshows
Creator
Jade Tan-Holmes
Script
Sheila Miller
Editing and Motion Graphics
Hamish Gilbert
Mental Image Productions
www.mentalimage.com.au
Junior Arruda
/ iamaduo
Music
www.epidemicsound.com/
open.spotify.com/artist/1D30m... - วิทยาศาสตร์และเทคโนโลยี
![MOBYE - มีใจทำไมไม่จีบ (ASAP) [Official MV]](http://i.ytimg.com/vi/dCOdz92FU18/mqdefault.jpg)
How can you CHOOSE the number of balls left in the vase at noon?
HINT BELOW
*What pairing are you using?
First reply, guess I'm lucky😃😃
I really loved the Russel's paradox video , I still ask question to myself: if there is a set A which includes all the things I don't know , then is set A part of set A?
I mean how can I know what I don't know?
I paused and am thinking; please wait
Psst! Jade, I think you forgot to pin this comment
@@mattiasselin4955 whoops thanks for telling me! Pinned :)
Lol, "I can't show you infinity because I'm on a budget"
... okay, it's a way to put it.
😁
I'm envious that your alter ego is called BLADE
Hunt's vampires on the side
Isn't your alter ego's name 'Ronin'?
hopefully she doesn't have one named Slade
Your alter ego could be BLED...it's even sort of medical.
@@thedamnedatheist bledlife crisis
"let's assume you forgot how to count" that was my day at work.
lmao, did you try switching off and on ?
Occasionally the TH-cam algorithm will throw you a gem … this is one of those times. Fantastic Channel! … and years’ worth of content to catch up on.
3:32 Syntax Error: Vsauce music expected.
Exactly my thought.
Glad I wasn’t the only one.
Backwards bent arm
And here I was at the end thinking “but hey, that’s just a theory...a MATH THEORY”
same, and I got so excited when I heard the new thinking music with the slick animation lol
“This not an infinite number of balls, I’m on a budget” The budget’s the only problem? SHE KNOWS SOMETHING WE DON’T 😂
Beauty AND Brains
She knows what BagelBoy described in a video named "pront"
A central bank extends her an unlimited credit line for "research purposes"...
Don't worry, the hyperinflation in the price of balls will get in he way long before she can buy enough balls to collapse into a black hole due to their mass...
^_-
Solution: Save one dollar to your bank, just reduce one cent.
Before Noon you are Billionaire, if the bank knows math well.
Each ball could be stored in that hotel with infinite rooms.
I’m impressed by how good her free hand drawing looked of the infinity symbol and on a curved surface.
I love your reaction when Blade comes in and say "my vase is empty". Your cold and somehow indifferent response although it's just a role play impersonation portraits a quite different trait of your personality.
Simp.
"I'm on a budget"
It is a failure from Jade to not plug in her Patreon ad there...
Time for a game of Universal Paperclips, but with numbered ping pong balls and vases
Blade is pairing up the balls taken out with the time steps. But what if Blade instead paired up sets of nine balls with the time steps?
Let’s say that she adds 10 balls and removes the first ball in the line, but then changes which set the first ball of every set belongs to to be the set before. e.g. at time step one she adds 10 balls and removes the first (sets are balls 2-10 = set 1); at time step 2 she adds 10 balls and removes the first ball in the line, which is ball 2, and shifts the assignment of the first ball in the newly added set so that it belongs in the first set (sets are balls 3-11 = set 1, balls 12-2 = set 2) etc. At noon, how many sets of nine balls does Blade have?
The mechanism is the same, but the answer is different depending on how you pair.
@@thinkgreatapethink Did you watch the whole video?
Zoltan haha I posted my comment in the wrong place. But yes I did watch the whole thing. My example differs from Jade’s in that as she points out she failed to create a one to one correspondence, whereas in my example a one to one correspondence is created between time steps and ball sets.
"Cow-nting"
Ha!
Moo-sic to my ears
Groan.... 😄😄
I heard this paradox before, but when you drew the relation to 1:1 pairing, that helped me understand it so much.
Blade :"My vase is empty"
Jade :"wat"
2:20
Let me rephrase that
Idiot trying to give a unnecessarily long metaphor: my vase is empty
Other idiot that will later give a unnecessarily long explanation: wat
@@generichomosapien4666 calm down its not that deep
Its too early in the morning for my brain to be hurting this much. I love this channel
it hurts, but in a good way
well, now that I have typed it.. please don't quote me '^^
I hate this channel
This is misinformation
Too many cows.
If nutrition and oxygen hurt you, you are numb for too long.
Well, it took a while but I did the maths, came up with 42.
It’s 69 bro.
😆
Maybe this question was really asking "what's 6x7"
Actually I feel like it would only take a minute.
Me, too, but I came up empty…
Dividing time an infinite number of times, you’d never get to noon. It’s like if you were trying to move along a ruler and you always moved half the distance, you’d never reach the end of the ruler because there’d always be more distance to travel
Exactly my thinking. If infitiy desn't end, the question "how many balls are in the vase at the end" just doesn't make sense. You can just as well ask "how much is god" and the answer won't be "0 Euro", nor "infinite Yen". It'll be "I've told you every week for a year to leave my sermon and if you come back next week I'll call the cops".
see what you just described is Zeno's paradox. The idea is that since you can divide the distance between the beginning in half an infinite number of times you will never reach the destination. lets use your example of the ruler. in the first step we move 6 inches, then in the next step we go 3 inches next we go 1.5 in so on and so forth. in practicality it is (1/2)+(1/4)+(1/8)+(1/16)... you claim that since you can keep moving half the distance you would never reach the end of the ruler. However this is false we can actually prove that (1/2)+(1/4)... is actually equal to 1
here's the mathematical proof
(1/2)+(1/4)... = y
2 x (1/2)+(1/4)... = 2y
1+(1/2)+(1/4)... =2y
multiplying (1/2)+(1/4)... by 2 results in 1+(1/2)+(1/4)... because (1/2)x2= (2/2) which is 1 and (1/4)x2= (2/4) which is (1/2) and so on and so forth
(1+(1/2)+(1/4)...) - ((1/2)+(1/4)...) = 2y - y
1=y and boom we have just proven that (1/2)+(1/4)... is equal to 1 (fun fact a very similar method actually proves that 1=0.999...)
if every step on the ruler took the same amount of time then it would take an infinite amount of time to reach the end but by doing something called a supertask we can actually do it in any finite amount of time.
lets say we want to walk across the ruler in 1 minute
we take the first step through half the ruler in half a minute AKA 30 seconds
then we do the second step across 1/4 of the ruler in 1/4 of the time AKA 15 seconds
we continue to do this and by the time 1 minute passed we would have crossed the ruler moving at the speed of 1 foot per minute
if you pay attention what she was doing is actually a supertask
if you don't believe me I would suggest doing your own research into this subject there are many great videos on this subject on this platform
@@sourcererseven3858 I suggest checking out some videos on "Zeno's Paradox" it deals with exactly this and the conclusion may surprise you
@@Tankirb What the proof states is not that 1/2+1/4+1/8... = 1, but that that Σ1/n+1 for n(1 -> ∞) approach 1. This is called a limit, and the limit of Σ1/n+1 for n(1 -> ∞) = 1
And 0.999 ≠ 1. Because what ratio of integers is 0.999... in which the numerator can be multiplied by 10? Rather it is that 1-1/10n approach 1 for n(1 -> ∞). This is also a limit.
@@axellinder2059 so would you say 1/3 * 3 = 0.999... then?
Hi Jade, This video blew my mind as virtually all your wonderful videos do. When l was midway through this part video, the Mandelbrot Set (MBS) came to my mind.... I thought, "wouldn't it be great if Jade did a video on that?" Then near the end, my mind was blown again when you actually showed a colorized MBS!
I wonder if you've done a video on the MBS? If so, l'd LOVE to see it. If not, might you consider making one on this amazing phenomenon?
P. S. THANK YOU for all that you do 🎉
I just imagine the store clerk ringing 20 ball containers and judging you silently
I wanted to relax and watch a video during my break and am now questioning reality
You think you have it bad? Imagine how Count von Count feels!
“Yes I know that infinity cannot be multiplied, added, subtracted... etc, but I’m just gonna ignore that”
Really creative way of making this paradox accessible. Loved it!
10:22 What makes infinity different is that it can only exist as a concept, infinity cannot exist anywhere within the finite phsyical unirverse, there is no infinity of material things.
Yea it's a fundamentally flawed question, just to exist as a little brain teaser that shouldn't be taken seriously. Not to mention needing to build up to an infinite speed to be able to move balls out of a container at infinite time divisions.
"I'm on a budget"
Oh, well, if that's the only thing holding you back... :')
We better all sign up to Curiosity Stream so she can do the video properly.
@@ReDFootY Assuming there's an infinite number of us, or at least one of us has an infinite budget.
Unfortunately I don't think anyone will ever have the budget and if by some miraculous chance someone does raise the required funds, they'll probably come up with some feeble excuse, like they don't have the time.
"If we treat time as infinitely divisible"
Discrete Time Theorists: "Fools!"
I mean, planck time is in fact a thing last time I checked
I think physicists are being a bit narrow-minded not being able to imagine infinitely divisible time ever since they invented planck time ;)
th-cam.com/video/J3xLuZNKhlY/w-d-xo.html in this video at 1:05 there's an simulation it is called as energy density of gluon field fluctuation ,now i wanted to know is this simulation an image of one of 17 quantum fields(i.e gluon-field)?
There is no infinities... they're just "tools"...
There is no infinite time, no infinite things, and so on...
Infinites are just a hack on math
@@fabriciocastrovizzotto9106 Planck time is just a unit of time as established through other fundamental constants, it is by no means a fundamental cap on the division of time, unlike, say, the quantisation of energy.
I thought the answer was just going to be something like “You’ll never reach noon, so who knows?” 😂
Thanks for the infinity trip, btw I understood less than half of it but I loved the video.
New sub, thanks again!
there are 42 balls in the vase.
😂😂😂
I know that reference.
When I started in aeronautical engineering and math, I had lots of trouble with infinity. At 76, infinity has no fears for me. Maybe I have unconsciously changed from being an engineer to a philosopher as I got older. How aircraft fly is still magical and how they can get a drone to fly on Mars is even more mystical.
I think the best way I heard infinity explained is from my high school math teacher. He said infinity isn't really a number, it's more of a direction on the number line
I love you ! your channel is one of my favs!
This is a variation of the Hilbert’s Hotel paradox. Both illustrate why a physical infinity is an impossible concept.
woah you’re here too! And in viva la dirt league
It is not. The paradox arises from the fact you cannot reach infinity via counting with finite numbers. For example, you can have an infinity universe model (current ones are finite though), but it could not be created from finite things, it could however exists ever.
Nope. They don't illustrate that a physical infinity is impossible. They illustrate that infinity is not a number or a quantity. And to treat them as a quantity by performing mathematical functions with the concept is to make a silly mistake.
We know that Space and Time are physical and real infinites because they are infinitely extended. We know they are infinitely extended not because we can observe it in their entirety, but because we can use a priori deduction to deduce it. Remember, Non Existence can never be. Therefore there can be no Non Existence that can delineate a spatial or temporal finitude to existence as a WHOLE. This a priori truth was pointed out by the great Parmenides, over 2,500 years ago. :)
Infinity should not be thought of as the largest possible number, but a number so arbitrarily large that we don’t care if something is slightly or even fractionally bigger or small most of the time, and then infinitesimals as the same except 1/infinity, which makes maths and stuff like L’Hopitals make much more sense when working with infinity, as in the paradox, as one of the infinities is “base infinity” and the other is ten times “base infinity”, so you subtract them. Its basically the same idea as Xeno’s arrow, which splits infinitesimal distances over infinitessimals at the same rate, so the arrows move even though theres an infinite amount of subdivisions, its happening in small subdivisions of time that are decreasing at the same rate. It also explains why some infinities are bigger than others, for example, you can take a line out of a plane, but not vice versa, so it would be base infinity vs (base infinity)^2. This explains a lot of paradoxes, as there is technically stuff higher than infinity, we just don’t care most of the time, so we consider it to be some sort of value to high for us to really care about the specifics most of the time. Then again, maybe this is too much of a nonanswer.
I tried to do this, but I wasn't fast enough.
Tomorrow, I'll start an hour earlier.
Every time you fail, double your speed on the next attempt. How fast do you need to go?
What I will say, though, is regarding infinity, the Mandelbrot Set illustrates infinity in a finite space. So that’s pretty cool. Love you, Jade. Never stop posting, please.
Your videos are so amazing!
3:13 Yeah, that's my facial expression for every paradox I've heard about...
This is my expression watching this video 😑
I like how you showed the infinity symbol and an impossible triangle side by side.
This is exactly what came to our mind when me and my friends designed a logo for our indie game studio, our slogan was "Everything out of Nothing", we wanted a zero and an infinity, we ended up drawing a rectangular zero that is also an impossible shape , then evolved it to a round zero that it also an impossible shape (kind of like a mobius strip).
In comparison, in calculus (and any good precalculus class) we learn that limit x->a f(x)-g(x) is an indeterminate form if and g both tend toward infinity as x tends toward a. But in many cases,.clever use of algebra and/or rules of limits allow us to calculate an answer. And in calculus you can use l'hôpital's rule if you can differentiate f and g (plus some other conditions)
This video is fantastic, I can't believe I just found your channel. I am looking forward to checking out your videos.
A more formal explanation: you're describing infinite sequences of sets of natural numbers. For the first example, S0 = {} (the empty set; the vase starts empty). S1 = {1..9}. S2 = {1..9, 11..19}, etc. We can say that this sequence of sets "converges" if, for every natural number, it eventually settles down and decides whether it's in the set or not.
That is, Sn converges to S' if for all natural numbers X, there's some N such that (X is in S(M) if and only if X is in S') for all M > N.
When we talk about "the contents of the vase at noon", we're really talking about the set to which the contents of the vase converges.
In the first example, for all X, X has decided whether it's in the vase or not by timestamp X/10 + 1. After that point, it will never change its mind. So, the first sequence converges to the set of all natural numbers not divisible by 10, which is an infinite set, so we say the vase "has an infinite number of balls" for short.
In the second example, for all X, X will decide that its out of the set as of timestamp X+1. After that point, it will never change its mind. So, the second sequence converges to the empty set, which is... uh, empty, so we say the vase has zero balls in it.
You are so good at explaining this plainly, great job and thank you!!
Finally, a video I grasped, sorta, well, kept up with, kinda.
Love these video's, even if I'm lost after the 1st few minutes.
I agree completely - as a phi nerd and a math nerd, I am positively _fascinated_ by the intersection between them. Many of my friends roll their eyes in a "there he goes again" look when I start talking about this :-)
“Assume time is infinitely divisible”
Now just hold up just one gol dang Planck Time Unit there, missy!
That’s not what’s going to get you into trouble here, but yes Planck time is a thing.
Can you expand on that? I am interested in this stuff.
@@Skibbityboo0580 The speed of light will be a factor long before you’re down to Planck scale. Suppose you need to move the balls 1 meter, then when there is 1/299792458 seconds left then you will not have time to complete the next cycle. So in reality there is not an infinite number of cycles. The paradox only appears because the physical limitations are not considered. But it’s still a fun topic.
You CAN divide the planck length it is just that its meaningless to in terms of events happening.
The word infinity should never be in the same sentence as assume.
" Maths and Physics would be limited without Infinity" Badum Tss :D Pun not intendes i guess?
Can we divide infinity into types?
1) Infinity extending on one side (eg- 1,2,3,4,5,...)
2) Infinity extending on two sides (eg- ...-3, -2, -1,0,1,2,3,... )
3) Infinite things between 2 things in an infinite line of things (eg- {Set of Rational numbers} or {Real Numbers}
The other thing I love about your channel besides how well you explain these fascinating math topics is your wonderful cultivated Australian accent
10:33 I guess everybody here asked this question to himself , well, when I asked this question to myself, when I was younger, my brain said 1 million and I be like okay👍
@Mr. Virtual no, you know the times , when you are talking to yourself, and someone answers,it's called introspection, and I said brain just for the meme
Watching your videos makes me smile
Thank you much for the lessons.😊
I love that animation of the ball rolling around the Penrose triangle!
I would suggest there's a contradiction in the original paradox in that you're directly linking an infinitely divisible continuous variable (the time stamp) with an indivisible discrete variable (the number of identical balls). Hence you get a contradiction to which either answer gives an incomplete answer.
Everytime I simulate this problem, the vase ends up shattered and broken. 🤓😅🤣
That's because we take the Tootsie Roll Pop approach. 1 2 3 hammer smack. Not correct but Infinitely more satisfying. 😆
"if we treat time as infinitely divisible" you said.
I would love to see a video of yours where you delve into continuity of time and space
Infinity! How well you explained it. Excellent
4:00 better not do this part during a pandemic. That many milkshakes will SURELY bring all the boys to the yard.
Awesome video!!! Thank you!
The problem comes from applying the word 'all' in 'pairing all elements of an infinite set'. 'All' or 'every' become semantically nonsensical when applied to infinity because you can't exhaust infinity.
Pairing does not require exhaustion. There are plenty of non paradoxical results that can be derived that involve a constructive pairing between two infinite sets.
@@FadkinsDiet No it doesn't, but pairing 'all' or 'every' element does entail exhaustion. That's why those words in conjunction with infinity are nonsensical.
It's still (+10n-n)=(+9n) at each step, so it doesn't really matter how many steps you take, the final result is still 9n, which is +infinite at the limit.
As you said, what the second method does is creating a 1:1 correspondence between the - removed - balls and the number of time steps.
The second method has completely forgone counting balls, even if it could have been possible to do it, exactly as it has been done in the first one by counting 9 balls for each step.
In the end, the two methods are exactly the same: the only difference is our attention is focused on two different things.
Exactly. Please scroll up and read the comment I made on November 11. I work out the mathematics. What is really annoying here is that there is so much misinformation in the world because somebody says something, somebody else hears it, tells it to somebody else, and it spreads to the whole world. Matt Parker (his youtube channel is Stand-up maths) states a slightly altered version of the problem, and his conclusion is that the box is empty, which is absolutely ludicrous. (Please check out my comment on his video about it. He posted his video on October 31. I work out the mathematics there also. Within the video, he describes adding and removing ping pong balls to a box in a specific manner). I wish people everywhere would get the word out to correct this. The Ross-Littlewood paradox, as I show in my comment, is nothing more that a modified version of a divergent series problem, or the way Matt Parker stated it, a conditionally convergent series problem. And yet, because the problem was first described decades ago by a well known and respected mathematician, people automatically (and blindly) think it must be true, even mathematicians and philosophers of today, which completely dumbfounds me. Wikipedia has an article about it that I read quickly last night, and in it they make a couple of ABSOLUTELY nonsensical statements regarding the problem as described.
Nicely done, charming presentation. I don't think I'll ever be good at maths, but it is still fascinating.
Hey! Did you sneak in and use my cloning machine without asking? 🤔 (Also, good video.)
Everyone is here. Love that my choice in TH-cam channels isn’t as unique as I thought :) also how do I decide whose link to use for nebula or curiosity stream when I want to attribute you all?
It’s not a clone; it was Blade
Nick, oh my gosh!
Hey Nick, what if the reason there is more matter than antimatter is because after both being created they got paired back in a different way such that they annihilate only the "even" matter, leaving behind the "odd" one. Just like the vases in this "paradox", one ends up empty and the otherone ends up full, like our universe. Of course for that to be the case, the universe would have to be infinite and there has to exist a pairing mechanism that results in a full vase (universe).
Can that be a theory?
@@victorvalencia6466 "huh. so... the real question is who put them there and why?"
This video reminded me of the fact that a conditionally convergent series can be rearranged such that their sum equals any number! Wonder if they are related.
kinda like the sum of the whole numbers equals -1/12.
That's just a rearrangement (admitidly not very rigourous at the time).
@@Tyranastrasza Actually, the sum being -1/12 is the most rigorous rearrangement, as setting it to that is useful in real physics and is requires for quantum field theory. Other possible arrangements don’t have this utility.
Looking forward to the future installments about Cantor and cardinality :-)
Thanks for being so smart and teaching us about numbers.
"I'm on a budget" 😆
Huh, I was thinking you were going to talk about the Doomsday Argument but I guess we can save the existential crisis for another day, just some good old fashioned Up and Atom brain melting!
(Just teasing of course, this was actually not too hard to follow)
Why is none commenting ? Also khanubis hi
@@KhAnubis Huh, KhAnubis is everywhere now, he has become one of us!
This video is unnecessarily long and this is misinformation, she stated that you can do inf- inf, but you cant, the answer is unidentified, not zero or infinity, very very bad video
@@generichomosapien4666 She didnt say inf minus inf. If you think what she presented and inf-inf is the same argument congrats, you are wrong.
Considering the material actions of both pairings are the same, it's interesting to think about abstracting out the counting method that 'changes' the outcome by one more layer. Suppose a machine was set up which performed one of the two methods, either removing the next multiple of ten ball or the next integer ball with a method that couldn't be easily discerned by the human eye - perhaps the balls are numbered with some infrared stamp or something. Is it possible to assign two different numbering systems to the same symbology such that the multiples of ten in one correspond to the natural numbers in the other? Both sets are, after all, the same size. What then would an observer working with each numbering system see when observing the same ball removal process?
My attention was caught by an infinity paradox while I was enjoying T rex tearing the sail of a spinosaur.🤣 Another great video J.
12:35 i thought its gonna be IS MATH RELATED TO SCIENCE
So amazing!!
Omg, your videos are soooo good
If time is infinitely divisible, you would never reach noon in this thought experiment.
Isn't the "correct" answer that you would actually never reach "noon" unless you at some arbitrary partition of "time" decide to round that partition up to twice itself?
There's an infinite amount of partitions
Yeah, at any given point in time you have a finite number of balls in there. But that defeats the purpose of this argument. You could just say that you keep on adding balls forever and leave the noon part out for that sake, to simplify it a little bit. Like you can't do something for forever ofc, but theoretical math can.
Just apply a limit
"Did I ever tell you the definition of Infinity?" -Vase
This video is good if you ignore
1. time can be infinity divided
2. You reach noon at some point
3. The vase is infinite
4. Infinity can be treated as a variable
5. Infinity is also a number not an idea
6. How she acknowledges that infinity is an idea and yet, still treats it as a number
7. So basically ignore the whole video and you should be good
At 2:00, well infinitely-divisible time is only an assumption, so I would count until Planck’s Time is reached and multiply that by 9.
Reminds me of series that can converge to any number depending on how you arrange the terms.
8:45 “We were both right”
That means 0=∞ and whole number line collapses to one single point
Wait ur right, 0-0=0 and 0+0=0
Just studied this yesterday in Probability. I asked myself, “Why didn’t anyone ever make a video about Ross-Littlewood Paradox?”.
Here’s Jade, just a few hours after!
Lotta Love as usual, Jade/Blade ❤️
Ross littlewood paradox belongs in the trash
The answer is unidentified
Enjoyed the video as always. Time and knowledge is relative to the scale that we are in. I feel, infinity is a concept that cannot be really debated as its more theoretical mathematics than practical.
Treat Infinity as a Variable, like x. But ALSO treat Infinity as the same number in all your equations. Granted the number is extraordinarily large but the same number, like you would treat x as the same number in all equations.
Add 10 and Subtract 1 an infinite amount of times
(10 -1)*oo
9*oo
9*oo is not oo. 9*oo is Nine times Infinity
In your first case, you pour out 9 times Infinity and Blades vase should have the same number of balls, 9*oo, so she shouldn't really run out before you do.
You mention a one-to-one correspondence. Yes oo's used in different equations should have a one-to-one correspondence. i.e. They should be equal.
All counting numbers is oo.
All counting numbers minus the first hundred is oo-100.
x = oo
y = oo - 100
Yes, y < x. Treat infinity like a Variable and combine equations and you have y = x - 100, so y is 100 less than x.
The two sets are not a one-to-one corresponded since the Infinity in the first set is not equal to Infinity in the second set.
All counting numbers is x = oo
All even counting numbers is e = oo/2
Treat oo like a Variable and combine equations: e=x/2
When treating oo like a Variable, you can continue to apply the "usual laws of arithmetic".
Many of the oo equations that I've experienced in college have a condition like "as x goes to infinity" and when you combine two equations like that, you may find that you end up with a finite number.
Example:
Limit as x -> oo of x is oo
Limit as x -> oo of 1/x is 0
Combine the two:
Limit as x -> oo of x * 1/x is x/x which is 1.
I have not encountered any equations where the oo cannot be treated as the same Variable. Of course if a variable goes to Infinity at a different rate, then include that rate in our equation to make Infinity the same.
I truly wish that the usual laws of arithmetic included treating Infinity as the same variable; big, but equal.
2:21 Blade appearing out of nowhere and just saying "my vase is empty" lol
To all those saying to “increases her budget.”
Increasing her budget to infinity would cause infinite inflation which would mean that the infinite amount of money she’ll be given will become worth close to 0.
You can't do that .... Lister left his light on so the Electric company and Lister are the only two surviving financial institutions (Red Dwarf)
But if she pays 17% of that in VAT and the ball producing company pays its infinite sales tax - Then the government will still get an infinite amount of tax revenue...
The rest of the population will be on an infinite amount of government paid benefits - But unfortunately the only thing that will get produced are yellow balls - but it's only a thought experiment... 😉🤣
There is a confusing mistake in the beginning of the video. You meant to say take out balls 1, 2, 3 NOT balls 10, 20, 30.
Amazing as always 😀👍
This video is the best reason for me to get curiositystream so I can watch your bonus videos on Nebula
The concept of infinity is fascinating
I always had the thought in my mind that if infinity and infinitesimal behave differently rules, why is the world so predictable? This question made me question myself so much I took physics at my university. Eventually, I realized infinity and infinitesimal in their full glory are just concepts and do not physically contribute to the world[I am pretty sure I framed this sentence so bad I seem a lunatic now]. Like we cannot have time smaller than Planck's time, cannot have speed more than the speed of light, cannot have accuracy beyond the Heisenberg principle. Every place where one could imagine bringing an infinite count or an infinitesimal count/accuracy, there is some rule of physics waiting to disappoint your idea.
To me, this seems to make the world predictable. I mean if the behavior of infinitesimal silicon atoms(yes, they are not. I'm just saying if they were) were different from time to time, I would not be sure if this was the exact message you were seeing. If neurons behaved at infinitesimal accuracy, I would not be sure I could control my feelings in front of my crush. And while some say it would have been great if there was one physical non-barrier to infinity; the idea that things are normalized, countable, quantized, discrete, understandable, fascinating really helps me sleep at night.
Apparently MY milkshake brings all the cows to a philosophical debate on infinity!?
Not the outcome I was hoping for but bever the less welcome.
Great conversation piece. And I was clear about it all until the summary.... If at step 1, you take out ball 10 and at step 2 you take out ball 20, etc.... wouldn't you have the same number of balls but numbered differently? You could still make matching sets with the 10, 20, 30 balls, to steps 1, 2, 3, right?
The issue isn't which balls are removed, its the logic behind how you draw your conclusion. It's such an interesting topic. I would love to hear your explanation about different infinities.
Oh, and I think math is a language used to describe and manipulate amounts. The value of the amount of blueberries is X, the value of the color of blueberries is blue (ish), the value of the name of that objects is "blueberry".
Damn, infinity is weird. Also, it will be from now on my explanation for everything.
- How can this series match every number?
- Infinity.
- How can a shore be so big?
- Infinity.
- Who ate the last piece of cake I was saving on the fridge?
- Infinity.
What should I reply?
Infinity
The coastline paradox, the smaller the measurement, the more detail, the longer...
time is more like a big ball of wibbly-wobbly, timey-wimey stuff
Started well, that sentence.
Ooh, bananas!
@@Hans-gb4mv ?
@@romainsavioz5466 I was actually hoping someone would pick up and post the next line of text. The quote you gave comes from the episode "Blink" of Doctor Who. The second run of the DVD, when they are in that old house is something that I still remember. Still, one of the better episodes imho even though it doesn't have much Doctor in it.
@@Hans-gb4mv I think it is the best episode, but I didn't remember the timey wimey quote was from that one.
My wife and I use that quote regularly 😁
In the correspondence between 1 to infinity and 101 to Infinity you can use the same example to show that 1 to Infinity is a longer list. You can do this because you gave each list item a numerical value. If you take list X (1-Infinity) and set aside numbers 1-100 you can then match the two lists together, list item value to list item value. Starting at 101 from list X matching to 101 of list Y and going forward they will all match for Infinity. However you will never find a match for the fist 1-100 of list X and in fact we know they are not on that list. So you can conclude that list X is longer then list Y. When you say its the wrong pairing and you needed to make the right pairing you are falsifying the data by leaving out important. In the X to E correspondence you must match the two to two and four to four leaving out the unmatched values. Those values are not on the list so it is a shorter list. They are both infinite but infinite is not a value that is always equal it simply means unending. So 9 times infinity is not Infinity its nine times Infinity, you can't reduce it.
Too long, sort answer: inf cannot be used as a variable, inf*inf=inf
Take your list X, numbers 1 to Infinity, and list E, numbers 1 to Infinity minutes all odd numbers. Now lets color all even numbers red and odd blue. If you make the correspondence of all the reds they will forever match up and you are left with ummatched blues. If you have list X, 1-infinity, and list Z, 1-infinity aswell. We now agree these list are equal containing a definitive one to one correspondence. If we take one item from one of the lists then we know it is one less. We can even identify it was item one from list X that we removed. Now a true correspondence would identify that item one from X is gone and leaves item one from list Z without a match. This shows the minus and only if you do the incorrect corresponding do the two infinities remain equal. So my point is that Infinity stands for never ending but the thing that doesn't end still has value so you can take from and add to that amount.
The obvious flaw in this logic (& presented by many others on youtube) is that infinity is treated as a number. Infinity is NOT a number.
e.g. at time stamp 5:50 y
The paradox comes from treating infinity as a number... it is not a number, it is an indication that something is wrong with the problem.
Infinity is a word, don't jumble numbers with words, im telling you, your brain can melt because of it...
You can have infinite numbers of many sizes and we dont tend to notate them with infinity symbol.
Infinity is a type of numbers.
Like whats the answer of integer/integer. And such error would call it =1.
Nope. Integers are different sizes, we dont know the answer. The particular integers we 9/3 so its 3 not 1.
Same with infinity, but we also kind of dont know the discrete numbers either, also could relate them to eachother by ratios or sets i guess.
"This isn't actually a real paradox"
Well I mean, it's a veridical paradox.
No it isn't. A veridical paradox is one where a truth seems untrue but is, in fact, true. This paradox arises from the manipulation of the infinite under application of finite logic and finite processes, resulting in contradiction. There's nothing "true" about the setup or the two contradictory results of the setup, regardless of the (arbitrary) rules of Transfinite Set Theory.
The seemingly absurd notion that both interpretations are valid and are not mutually exclusive is the veridical paradox.
@@AstroTibs The interpretations are not actually valid as there is nothing real about the scenario. That's where the contradiction between the two seemingly equal results lies. Again, you can't manipulate infinite quantities as finite quantities just because you can interchange them verbally. A finite quantity is an inherent definable property with definite boundaries. An "infinity" is not. They are categorically different things.
This is one of those beautiful cases where the limit and actual infinity diverge. cause in the limit, as we approach infinity, we are building up infinite balls, yet if we do this process for every number on the number line, we end up with no balls at all.
11:28 Not many cosmologists really believes anymore that the universe will do the "big crunch" - on the contrary: vast majority believe rather the heat death or "big rip"...
What is even going on here?
You made me remember why I quit Maths after my High school. 🤣
I'm still wondering how Blade is able to identify and remove ball _x_ in an infinitely small sliver of time when I can spend 10 minutes looking for my keys and not realise that I've got them in my pocket.
The powers of an ideal mathematician/physicist.
Thought-experimentation might be the wrong method for locating car keys?
yeah, it must be harder and harder every time to find the ball each step.
I immediately though that it would take infinite time to find the balls eventually, so the jug would be filled.
But I'm just a computing scientist pretending to be mathematician.
@@JindraAG oh, the powers of spherical cows
i have a different solution i might be wrong but please tell me where i wrong at
so if i take out ball 1 and then 2 and 3 ... it should still be the same as i take out ball 10 and then 20 and then 30 cause {1,2,3,4,5...} is equal to {10,20,30,40,...}(both are infinity) so both vase should be empty right ?
(sorry for my bad english)
I got side-tracked around 4:20, appropriately enough. Now all I want is to share a milkshake with a cow.
MooOOOOoooo
Thank you
You're welcome
Mathematical justification to blast, "Big Balls" by AC/DC
1:01
Infinite balls because we never reach noon