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?
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... ^_-
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.
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.
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.
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.
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
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.
ruclips.net/video/J3xLuZNKhlY/видео.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)?
@@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.
The fallacy is that the definition of comparable states is that you wait until you have compared all the elements in the sets. when you finish, While with the infinite sets you ignore this requirement by trying to predict what the outcome will look like and accepting that answer if it sounds logical without providing proof of the logic that lead to your answer when you have finished grouping them, but with a infinite set, you can never finish grouping them so you never come to your decision point you are basing your answer on. To put it more, simply you never meet all the requirements of your comparison method because you always have more cups of chocolate to hand out and more cows wanting chocolate.
The fallacy is that people try to calculate the cardinality of the "limit" of a sequence of sets by taking the limit of the cardinalities of the sets. But you cannot always interchange the order of operations if you are working with limits.
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
@@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.
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.
This task feels like the type of thing Superman would do in the comics lol. Something like: Batman: Hey Clark, what's going on? Superman: Nothin' much, just sorting infinite balls into a jar before noon. What are we doing for lunch?
division and individuality are arbitrary ideas, which is a way of saying that math is just an arbitrary idea like a language. languages aren't absolute but they can still convey meaningful and true ideas but they fall short in many cases as well, so does math.
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).
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.
This seems about as stupid as "You observe one person enter a building and then two exit. If one more person enters the building then it will be empty (1-2+1=0)". The two sets might have some kind of equivalence but the way the problem is described there is no point in time ever where there are 0 balls in the vase. It is always growing faster than it is shrinking. Either your math is broken or it's useless for modeling anything in the physical world. It seems that your choice of applying set theory to figure out how to model this related rates problem at infinity is not a good one, and it hints that perhaps not all infinities are equivalent.
Everyone is here. Love that my choice in RUclips 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?
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?
@@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.
4:09 Obviously there would be infinite balls both inside and outside the vase but lemme explain. An infinite number of balls are put in the vase in sets of ten and for each set, one ball is taken back out. Since more were left in than taken out, there are still infinite balls remaining inside the vase. But since one ball was removed each time ten were added and this was done an infinite number of times, that obviously means there are also still infinite balls on the outside too. Shouldn't that be basic math? I don't understand how that could have been considered a paradox.
I should also mention though that because time was infinitely divided in order for balls to be moved an infinite number of times before 12:00,.... well that means twelve o clock never came because infinite time happened before twelve o clock. Therefore the experiment never ended and the person doing it would continue adding and taking balls within ever increasingly shorter amounts of time for the rest of all eternity as twelve o clock ⏰ technically gets further and further away from them.
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
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}
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"...
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 🎉
- Just sharing my idea at 5:36 so haven't watched the "fun" part yet - I don't see a paradox here. In the second case, you have infinitely many balls too. Of course you can tell when a specific ball is taken out of the vase, but I can't reasonably specify every one of the infinitely many balls. The first ball that stays in the vase already has infinity written on it (you probably lost count I guess), and the last one too. I mean it's kinda like saying there are no sharks in that sea, and trying to prove it with the fact that I don't even know what a shark is. But let me also go one step back, because in fact, there is no way you have no balls left in your vase. For every timestamp, you take out one, and put in 10. If we are checking at noon, then we are (somehow) over with the throwing balls around, so there was a LAST timestamp, when you put in 10 balls, and took out one. It doesn't matter what was the ball count before, given that you can't have negative amount of balls, you are always going to have at least 9 balls in the vase.
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!
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
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.
@@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.
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
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.
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
1:29 No, I can't agree. When you start applying physical constraints (especially infinitesimal time) to a mathematical process (ala infinite sum: Zeno much?) the results are not assured - not to mention conflating the resultant possible infinity as a number.
It's not a paradox. The answer to the first question is infinity - 1. The answer to the secondary argument, where she just sequentially removed the balls, starting at 1,2,3 etc.... is still infinity - 1. The balls that remain always outnumber the balls that were removed, infinitely, due to the initial equation. To help you better understand why pairing the sets is irrelevant, just think of the initial visual she created in the video, and wipe the numbers off the balls. The pairing, the "label" of each number is technically irrelevant. It's has no more meaning than the number being a co-ordinate, but it doesn't give each individual number more or less value. a single ball is a single ball, be it the first, or the billionth in a set. This is what happens when you start a thought experiment, that is quickly nullified, once you introduce "and divide it by 2, infinitely"
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.
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.
@@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.
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.
@@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.
8:35 It means that 1:1 correspondence in conjunction with infinites don't prove anything, except when a = b, where a and b are infinite, and a b (a is never different from b)
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.
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... 😉🤣
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.
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.
2:58 What about ball 3,000,436? Is that still in there? Well no, that was taken out on the 3,000,436th step... when I added balls: 30,004,351; 30,004,352; 30,004,353; 30,004,354; 30,004,355; 30,004,356; 30,004,357; 30,004,358; 30,004,359; 30,004,360..... Well weren't all 10 of those balls taken out? Well yeah, when I added 90 more because there's a 1:1:9 correspondence of [steps] to [balls removed] to [balls added] since every ball you can name has a corresponding step removing it AND 9 more corresponding balls YOU CAN ALSO NAME. With complete sincerity, I love ALL of your videos and I really appreciate your contribution to the internet as a whole. I just have a pet peeve when it comes to explaining infinity because despite the fact that infinity is mathematically sound, -attempting- to rationalize it with mathematical logic just does not work because MATH does not work on infinity. LOGIC does not work on infinity. It's literally incompatible. You can't add, subtract, divide or multiply infinity; You also can't reason with it, and It can't be manipulated in any way. I personally believe infinity can't be taught.... traditionally. Rather than speaking about what it is, I feel the only way to really talk about it is to talk about all the ways infinity DOES'NT interact with math. It's like how black holes interact with physics :D
Ball labelled 3,000,436 was NOT taken back out. Ball 3,000,440 was. Ball 1,000,000,000 was taken back out but the 9 before it and 9 after it weren't. Bucket is growing faster than it's shrinking. There is more than one kind of infinity so this isn't a paradox. What am I missing?
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.
Rewording Zeno's paradox. The answer is simple. You can add a infinite number of decreasing fraction and still arrive at a finite number. We call it calculus.
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.
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.
Two solutions (1) you can integrate infinitely small parts to get a finite sum (2) Time is not infinitely divisible. Plancks time is the smallest possible division of time. This is version of Zeno,s paradox.
Okay...sooooooooo... first of all, let me get realistic factors out of the way. Neither time nor space are infinitely divisible: there are Planck lengths and Planck instants, and those are pretty much how our mathematical probabilistic quanta work. Light has a 100% chance of moving onto another Planck voxel in the next Planck instant, and anything going at a lesser speed has a lower chance of doing that. (and dang I just realised that if you compressed yourself too much by going too closely to the speed of light, space itself would push you apart as if you were pushed against a wall by a very heavy force. Either that, or Planck lengths would compress, but then what would be the point? We have special relativity for god's sake.) That means you can't do this in real life, because eventually you'd stop. So we have to do it mathematically. Doing this, is like, doing it every minute for eternity. Now, it's kinda not possible to reach an infinite value using only finite numbers, unless you have infinity of them already - in which case, you pretty much have infinite numbers. That means, to finish doing this, you have to get to the end of eternity. Sounds crazy, right? Imagine eternity having an end - that ruins the whole concept of eternity! So I'm going to explain what infinity even actually is. I kinda wrote it somewhere on a video about infinitesimals but I stopped so I'm gonna have to get back to it again. Okay, so, real numbers (boi don't get me started by complex numbers, but I assume they'd start with rectangles) can be defined as a line segment with one end on 0 and the other end at where their value is. Obviously this has a bunch of applications, you can shift the points to get differential values or just measure the length of them to get absolute values, but basically, that's how it works. Positivity is a direction, right? (By the way, that's exactly why infinitesimals are not basically zero - mostly because they're positive.) Well, infinity just basically has a point at zero, and a direction leading toward high positive numbers. It doesn't have the other point. It's a line semisegment and it's pretty much the difference between a vector and a scalar (yeah I didn't get too far into that cram book about physics). So if you were to shift the points one up, would you be adding one because all of the line would be shifted one up, or subtracting one because you just moved the line one up without doing anything to infinity? Neither. Like I said, you can't reach an infinite value using only finite numbers, and I'll be darned if you can do anything to infinity using only finite numbers. I mean, you could use a negative hyperoperation and use an infinite number in it (the result of ∞÷∞ is the set of all numbers (every single one) between an infinitesimal and infinity, and the result of ∞-∞ is pretty much the set of all real and hyperreal numbers between negative infinity and infinity), but I cheated because I used infinity somewhere in both entries (although it does raise the question of what the heck an infinite hyperoperation would be like). If you were to do it mathematically in a finite fashion, then, well, you'd never end. Having an infinite series pretty much is a cheap excuse to get to the bottom of it, but since you can do that in mathematics, let's try. Okay, so, uh...when Jade does it, she ends up with a set of integers multiplied by 10, and when Blade does it, uh, well, she has an infinite supply of balls, so since ∞+∞=∞ then ∞-∞ will contain infinity as well. So what she'll do, is, she'll...don't you see? If she REALLY has infinite balls, then somewhere in an inaccessible pseudospace, she'll have an infinite supply of balls marked with the simple lemniscate as well. So do you know what she'll have if she tries? Assuming she does in fact get to the end of the stock, which incidentally doesn't exist, she'll have a set of integers, and pretty much drop off at infinity. She'll have infinitely many balls she didn't use and infinitely many balls marked ∞ she did use. I mean, since ∞×∞=∞ as well, the most basic infinities are really nothing compared with true infinities (although I only believe in different types of infinities because of divisions like countable and uncountable infinity (and that was after the explanation)). Honestly, uh, well, I'm still assuming they're humans, so let's replace them with mathematical variables with their names. Well, uh, yeah, Jade would still have that set, but what about Blade? I mean, I know she eventually takes away every number from the jar, but I'm still thinking finite here. She puts 9 times as many numbers in the jar EVERY TIME she makes that happen. I think we can all agree that ∞+1=∞. See? No difference. Although, some mathematicians don't - like they think that, uh, what's the symbol? **checks **ruclips.net/video/TCy6r3XOzqc/видео.html** They think that ω is different from ω+1. Personally, I think they're all lunatics for thinking you can just add one to infinity and make it larger than it already is. I mean, since ∞×∞=∞, and you can pretty much match an infinite set of any division of finite numbers to a set of integer or even infinitesimal numbers, infinity contains itself, STILL. (Oh and they also think there are nigh-infinite numbers, but I think they're -even bigger- lunatics. I think they should just put their math into making Touhou bullet patterns - then we can have a lot more interesting patterns than just flowers and spark patterns. I've seen those random mathematical art simulation projects on RUclips and Scratch.) So I think the idea that ω is any different from ω+1 is preposterous. I mean, I spent so long I forgot what point I was going to type here other than the one people already disagree with, but like...come on. Just...WHY??? Like it's so insane, think about it. Infinity doesn't end. Assuming Blade reaches it (and oh yeah, that's the variable in the scenario), she'll still have an infinite number of balls she didn't use because if she used them all, well, that's just silly. Uh, so, ｏｋａｙ ｗｈｅｒｅ ｔｈｅ ｈｅｃｋ ｗａｓ Ｉ okay so let me type this again _Blade_ repeatedly puts 10 balls into the set _jar_ and takes one ball out every time infinitely. And since it's an infinite series, she's forced to stop. That's one way I can prove that she has infinite infinity balls she didn't use. I mean, if the set ended, that...uh...yeah that would, uh, pretty much defeat the point of infinity. Damn it I'm still having trouble visualising Okay, the argument. At the end, she eventually returns every ball. Even though she put another 9 in there every time. I still think you're thinking finitely...? I mean, when she gets to infinity, she'll have 9 times the infinite balls in there. And, like, 9×∞=∞. Uh, so, once she gets to that pseudospace, I think there'll be a big hole of balls that went to _jar_ with no exact point of starting. So it's very blurry. no actually scratch it. it's a blur with no boundaries whatsoever. We're already in the pseudospace and this is infinity we're talking about. So there'll be an infinite set starting at 1 with the balls she returned, and an infinite set starting at infinity with the balls she left in the jar. There. That's my answer. Bye now. (also of course Blade would think there's nothing in the jar - it has infinite hammerspace, so she wouldn't even be able to hear the infinite balls of infinity tumbling down as a result of her tipping it down lol)
0:30 This is actually incorrect and the answer to your question would be "infinitely many". But if you remove "ball 1", "ball 2" etc instead of "ball 10", "ball 20" etc, the answer is not that easy. It would be "infinitely many" because for each ball taken you added 10 balls and at the same time none because for each ball you can tell the exact time when you took it out and that time is before noon.
If at time-step n you remove ball # n(10), then there *is* a 1:1 correspondence between the time-steps and the number of balls removed. Infinity balls in, infinity balls out. Also, the paradox is in the attempt to apply discrete, finite numbers to an infinite process. After all, with infinite time-steps, there is no "last" step, which means the last ball in the vase is never removed.
I think that's the right idea. We can't look at infinity. We can only look at the limit of balls as it approaches infinity. As we do that there is an infinite number of balls in the vase. That's it.
I think the vase can not be empty because when u do 1 step u add 10 and remove 1 so we have 9 and for 4000000th time we add 10 and remove the 4000000th so there are still 9 more balls.
There's a limit for dividing time with the Planck time. Therfore the amount of balls is finite. Altough very large. I'm sadly way too lazy to do the math and it would likely break my calculator.
2:35 “I thought you said to remove ball 1 at the fist time step and ball 2 at the second time step and…” No. She said to remove 10. Then 20. Then 30. Etc.
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.
You like paradoxes and I think that contagious cause I have started thinking about paradoxes. Should I drop RUclips premium and get curiosity stream? Streaming is the paradox of cable.
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 :-)
Not a philosopher. Not a physicist. I live on the street and I'm very happy. I remember realizing that all things in the universe are on the cusp of two infinities. The infinitely small and the infinitely large. So there you are. Another paradox. And Jade, can't afford Nebula but love you on RUclips
I love the concept of infinity. It has fascinated me for years now. I really really hope scientists will discover new facets of it still during my lifetime so I too may know of them while I'm around. I wonder how infinity would work in a math system that isn't based on counting, but something else.
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
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.
"let's assume you forgot how to count" that was my day at work.
lmao, did you try switching off and on ?
@@agnbfdgdfhow do u turn off something that's already off
@@CuongTruong-cb3mk Off +1, then off +2, then off + 3, ....
I’m impressed by how good her free hand drawing looked of the infinity symbol and on a curved surface.
“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.
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
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…
Occasionally the RUclips algorithm will throw you a gem … this is one of those times. Fantastic Channel! … and years’ worth of content to catch up on.
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.
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.
"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
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”
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.
"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 ;)
ruclips.net/video/J3xLuZNKhlY/видео.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.
The fallacy is that the definition of comparable states is that you wait until you have compared all the elements in the sets. when you finish, While with the infinite sets you ignore this requirement by trying to predict what the outcome will look like and accepting that answer if it sounds logical without providing proof of the logic that lead to your answer when you have finished grouping them, but with a infinite set, you can never finish grouping them so you never come to your decision point you are basing your answer on.
To put it more, simply you never meet all the requirements of your comparison method because you always have more cups of chocolate to hand out and more cows wanting chocolate.
The fallacy is that people try to calculate the cardinality of the "limit" of a sequence of sets by taking the limit of the cardinalities of the sets. But you cannot always interchange the order of operations if you are working with limits.
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?
"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.
I just imagine the store clerk ringing 20 ball containers and judging you silently
there are 42 balls in the vase.
😂😂😂
I know that reference.
This task feels like the type of thing Superman would do in the comics lol. Something like:
Batman: Hey Clark, what's going on?
Superman: Nothin' much, just sorting infinite balls into a jar before noon. What are we doing for lunch?
division and individuality are arbitrary ideas, which is a way of saying that math is just an arbitrary idea like a language.
languages aren't absolute but they can still convey meaningful and true ideas but they fall short in many cases as well, so does math.
Agreed
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).
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?
3:13 Yeah, that's my facial expression for every paradox I've heard about...
This is my expression watching this video 😑
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.
Actually, the universe may well be infinitely large.
This seems about as stupid as "You observe one person enter a building and then two exit. If one more person enters the building then it will be empty (1-2+1=0)". The two sets might have some kind of equivalence but the way the problem is described there is no point in time ever where there are 0 balls in the vase. It is always growing faster than it is shrinking. Either your math is broken or it's useless for modeling anything in the physical world. It seems that your choice of applying set theory to figure out how to model this related rates problem at infinity is not a good one, and it hints that perhaps not all infinities are equivalent.
Hey! Did you sneak in and use my cloning machine without asking? 🤔 (Also, good video.)
Everyone is here. Love that my choice in RUclips 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?"
“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?
I thought the answer was just going to be something like “You’ll never reach noon, so who knows?” 😂
4:09 Obviously there would be infinite balls both inside and outside the vase but lemme explain.
An infinite number of balls are put in the vase in sets of ten and for each set, one ball is taken back out. Since more were left in than taken out, there are still infinite balls remaining inside the vase.
But since one ball was removed each time ten were added and this was done an infinite number of times, that obviously means there are also still infinite balls on the outside too.
Shouldn't that be basic math?
I don't understand how that could have been considered a paradox.
I should also mention though that because time was infinitely divided in order for balls to be moved an infinite number of times before 12:00,....
well that means twelve o clock never came because infinite time happened before twelve o clock.
Therefore the experiment never ended and the person doing it would continue adding and taking balls within ever increasingly shorter amounts of time for the rest of all eternity as twelve o clock ⏰ technically gets further and further away from them.
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. 😆
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
This video is the best reason for me to get curiositystream so I can watch your bonus videos on Nebula
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}
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"...
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 🎉
You are so good at explaining this plainly, great job and thank you!!
"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
4:00 better not do this part during a pandemic. That many milkshakes will SURELY bring all the boys to the yard.
- Just sharing my idea at 5:36 so haven't watched the "fun" part yet -
I don't see a paradox here. In the second case, you have infinitely many balls too. Of course you can tell when a specific ball is taken out of the vase, but I can't reasonably specify every one of the infinitely many balls. The first ball that stays in the vase already has infinity written on it (you probably lost count I guess), and the last one too. I mean it's kinda like saying there are no sharks in that sea, and trying to prove it with the fact that I don't even know what a shark is.
But let me also go one step back, because in fact, there is no way you have no balls left in your vase. For every timestamp, you take out one, and put in 10. If we are checking at noon, then we are (somehow) over with the throwing balls around, so there was a LAST timestamp, when you put in 10 balls, and took out one. It doesn't matter what was the ball count before, given that you can't have negative amount of balls, you are always going to have at least 9 balls in the vase.
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.
2:21 Blade appearing out of nowhere and just saying "my vase is empty" lol
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.
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
If time is infinitely divisible, you would never reach noon in this thought experiment.
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.
"I'm on a budget" 😆
"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
1:29 No, I can't agree. When you start applying physical constraints (especially infinitesimal time) to a mathematical process (ala infinite sum: Zeno much?) the results are not assured - not to mention conflating the resultant possible infinity as a number.
It's not a paradox. The answer to the first question is infinity - 1.
The answer to the secondary argument, where she just sequentially removed the balls, starting at 1,2,3 etc.... is still infinity - 1. The balls that remain always outnumber the balls that were removed, infinitely, due to the initial equation. To help you better understand why pairing the sets is irrelevant, just think of the initial visual she created in the video, and wipe the numbers off the balls. The pairing, the "label" of each number is technically irrelevant. It's has no more meaning than the number being a co-ordinate, but it doesn't give each individual number more or less value. a single ball is a single ball, be it the first, or the billionth in a set.
This is what happens when you start a thought experiment, that is quickly nullified, once you introduce "and divide it by 2, infinitely"
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.
@jorgepeterbarton Nope
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
12:35 i thought its gonna be IS MATH RELATED TO SCIENCE
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.
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.
Well we all know jade is best
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 😁
"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.
First problem: You can never reach noon.
8:35 It means that 1:1 correspondence in conjunction with infinites don't prove anything, except
when a = b, where a and b are infinite, and a b (a is never different from b)
-still like chu.
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... 😉🤣
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
What is even going on here?
You made me remember why I quit Maths after my High school. 🤣
2:58
What about ball 3,000,436? Is that still in there?
Well no, that was taken out on the 3,000,436th step... when I added balls: 30,004,351; 30,004,352; 30,004,353; 30,004,354; 30,004,355; 30,004,356; 30,004,357; 30,004,358; 30,004,359; 30,004,360.....
Well weren't all 10 of those balls taken out?
Well yeah, when I added 90 more because there's a 1:1:9 correspondence of [steps] to [balls removed] to [balls added] since every ball you can name has a corresponding step removing it AND 9 more corresponding balls YOU CAN ALSO NAME.
With complete sincerity, I love ALL of your videos and I really appreciate your contribution to the internet as a whole. I just have a pet peeve when it comes to explaining infinity because despite the fact that infinity is mathematically sound, -attempting- to rationalize it with mathematical logic just does not work because MATH does not work on infinity. LOGIC does not work on infinity. It's literally incompatible. You can't add, subtract, divide or multiply infinity; You also can't reason with it, and It can't be manipulated in any way. I personally believe infinity can't be taught.... traditionally. Rather than speaking about what it is, I feel the only way to really talk about it is to talk about all the ways infinity DOES'NT interact with math. It's like how black holes interact with physics :D
Ball labelled 3,000,436 was NOT taken back out. Ball 3,000,440 was. Ball 1,000,000,000 was taken back out but the 9 before it and 9 after it weren't. Bucket is growing faster than it's shrinking. There is more than one kind of infinity so this isn't a paradox. What am I missing?
"I'm on a budget"
Lol I loved that
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...
This is how the government gets your money, yet always seems to increases the national debt.
1:01
Infinite balls because we never reach noon
“any number of balls can be left in the vase at noon” idk about that, good luck leaving π balls in the vase at noon.
HAHAHAHAHAHA
"My milkshake brings all cows to the yard / I can teach you, and there is no charge"
Rewording Zeno's paradox. The answer is simple. You can add a infinite number of decreasing fraction and still arrive at a finite number. We call it calculus.
Or till your hands reach the speed of light
"The answer is simple."
Then why is the explanation you gave totally irrelevant to the question?
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.
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.
You would never reach noon. So it would be impossible to determine how many balls there would be.
alter-Jade = Blade.
I don’t trust that Blade, she looks shifty ;)
I was right , it's about infinity 😃😃
Two solutions (1) you can integrate infinitely small parts to get a finite sum (2) Time is not infinitely divisible. Plancks time is the smallest possible division of time. This is version of Zeno,s paradox.
Rather the paradox shows that infinite summation of limits need to give the same answer as the limit of infinite summations.
Paradox: same setup, but each step you put in 10 and take out 9
If you assume the time can be divided infinitely small you never reach noon. The number of ball would approach infinite.
0:22 ''I'm on a budget'', well if you ask Elon Musk he will say the same thing
Okay...sooooooooo...
first of all, let me get realistic factors out of the way. Neither time nor space are infinitely divisible: there are Planck lengths and Planck instants, and those are pretty much how our mathematical probabilistic quanta work. Light has a 100% chance of moving onto another Planck voxel in the next Planck instant, and anything going at a lesser speed has a lower chance of doing that. (and dang I just realised that if you compressed yourself too much by going too closely to the speed of light, space itself would push you apart as if you were pushed against a wall by a very heavy force. Either that, or Planck lengths would compress, but then what would be the point? We have special relativity for god's sake.) That means you can't do this in real life, because eventually you'd stop. So we have to do it mathematically.
Doing this, is like, doing it every minute for eternity. Now, it's kinda not possible to reach an infinite value using only finite numbers, unless you have infinity of them already - in which case, you pretty much have infinite numbers. That means, to finish doing this, you have to get to the end of eternity. Sounds crazy, right? Imagine eternity having an end - that ruins the whole concept of eternity! So I'm going to explain what infinity even actually is. I kinda wrote it somewhere on a video about infinitesimals but I stopped so I'm gonna have to get back to it again.
Okay, so, real numbers (boi don't get me started by complex numbers, but I assume they'd start with rectangles) can be defined as a line segment with one end on 0 and the other end at where their value is. Obviously this has a bunch of applications, you can shift the points to get differential values or just measure the length of them to get absolute values, but basically, that's how it works. Positivity is a direction, right? (By the way, that's exactly why infinitesimals are not basically zero - mostly because they're positive.) Well, infinity just basically has a point at zero, and a direction leading toward high positive numbers. It doesn't have the other point. It's a line semisegment and it's pretty much the difference between a vector and a scalar (yeah I didn't get too far into that cram book about physics). So if you were to shift the points one up, would you be adding one because all of the line would be shifted one up, or subtracting one because you just moved the line one up without doing anything to infinity? Neither. Like I said, you can't reach an infinite value using only finite numbers, and I'll be darned if you can do anything to infinity using only finite numbers. I mean, you could use a negative hyperoperation and use an infinite number in it (the result of ∞÷∞ is the set of all numbers (every single one) between an infinitesimal and infinity, and the result of ∞-∞ is pretty much the set of all real and hyperreal numbers between negative infinity and infinity), but I cheated because I used infinity somewhere in both entries (although it does raise the question of what the heck an infinite hyperoperation would be like). If you were to do it mathematically in a finite fashion, then, well, you'd never end. Having an infinite series pretty much is a cheap excuse to get to the bottom of it, but since you can do that in mathematics, let's try.
Okay, so, uh...when Jade does it, she ends up with a set of integers multiplied by 10, and when Blade does it, uh, well, she has an infinite supply of balls, so since ∞+∞=∞ then ∞-∞ will contain infinity as well. So what she'll do, is, she'll...don't you see? If she REALLY has infinite balls, then somewhere in an inaccessible pseudospace, she'll have an infinite supply of balls marked with the simple lemniscate as well. So do you know what she'll have if she tries? Assuming she does in fact get to the end of the stock, which incidentally doesn't exist, she'll have a set of integers, and pretty much drop off at infinity. She'll have infinitely many balls she didn't use and infinitely many balls marked ∞ she did use. I mean, since ∞×∞=∞ as well, the most basic infinities are really nothing compared with true infinities (although I only believe in different types of infinities because of divisions like countable and uncountable infinity (and that was after the explanation)). Honestly, uh, well, I'm still assuming they're humans, so let's replace them with mathematical variables with their names. Well, uh, yeah, Jade would still have that set, but what about Blade? I mean, I know she eventually takes away every number from the jar, but I'm still thinking finite here. She puts 9 times as many numbers in the jar EVERY TIME she makes that happen. I think we can all agree that ∞+1=∞. See? No difference. Although, some mathematicians don't - like they think that, uh, what's the symbol? **checks **ruclips.net/video/TCy6r3XOzqc/видео.html** They think that ω is different from ω+1. Personally, I think they're all lunatics for thinking you can just add one to infinity and make it larger than it already is. I mean, since ∞×∞=∞, and you can pretty much match an infinite set of any division of finite numbers to a set of integer or even infinitesimal numbers, infinity contains itself, STILL. (Oh and they also think there are nigh-infinite numbers, but I think they're -even bigger- lunatics. I think they should just put their math into making Touhou bullet patterns - then we can have a lot more interesting patterns than just flowers and spark patterns. I've seen those random mathematical art simulation projects on RUclips and Scratch.) So I think the idea that ω is any different from ω+1 is preposterous. I mean, I spent so long I forgot what point I was going to type here other than the one people already disagree with, but like...come on. Just...WHY??? Like it's so insane, think about it. Infinity doesn't end. Assuming Blade reaches it (and oh yeah, that's the variable in the scenario), she'll still have an infinite number of balls she didn't use because if she used them all, well, that's just silly. Uh, so, ｏｋａｙ ｗｈｅｒｅ ｔｈｅ ｈｅｃｋ ｗａｓ Ｉ
okay so let me type this again
_Blade_ repeatedly puts 10 balls into the set _jar_ and takes one ball out every time infinitely. And since it's an infinite series, she's forced to stop. That's one way I can prove that she has infinite infinity balls she didn't use. I mean, if the set ended, that...uh...yeah that would, uh, pretty much defeat the point of infinity. Damn it I'm still having trouble visualising
Okay, the argument. At the end, she eventually returns every ball. Even though she put another 9 in there every time. I still think you're thinking finitely...? I mean, when she gets to infinity, she'll have 9 times the infinite balls in there. And, like, 9×∞=∞. Uh, so, once she gets to that pseudospace, I think there'll be a big hole of balls that went to _jar_ with no exact point of starting. So it's very blurry. no actually scratch it. it's a blur with no boundaries whatsoever. We're already in the pseudospace and this is infinity we're talking about. So there'll be an infinite set starting at 1 with the balls she returned, and an infinite set starting at infinity with the balls she left in the jar. There. That's my answer. Bye now.
(also of course Blade would think there's nothing in the jar - it has infinite hammerspace, so she wouldn't even be able to hear the infinite balls of infinity tumbling down as a result of her tipping it down lol)
0:30 This is actually incorrect and the answer to your question would be "infinitely many". But if you remove "ball 1", "ball 2" etc instead of "ball 10", "ball 20" etc, the answer is not that easy. It would be "infinitely many" because for each ball taken you added 10 balls and at the same time none because for each ball you can tell the exact time when you took it out and that time is before noon.
2:30 Exactly :D Good trick in your video :lol:
If at time-step n you remove ball # n(10), then there *is* a 1:1 correspondence between the time-steps and the number of balls removed. Infinity balls in, infinity balls out.
Also, the paradox is in the attempt to apply discrete, finite numbers to an infinite process. After all, with infinite time-steps, there is no "last" step, which means the last ball in the vase is never removed.
I think that's the right idea. We can't look at infinity. We can only look at the limit of balls as it approaches infinity. As we do that there is an infinite number of balls in the vase. That's it.
I think the vase can not be empty because when u do 1 step u add 10 and remove 1 so we have 9 and for 4000000th time we add 10 and remove the 4000000th so there are still 9 more balls.
There's a limit for dividing time with the Planck time. Therfore the amount of balls is finite. Altough very large. I'm sadly way too lazy to do the math and it would likely break my calculator.
2:35 “I thought you said to remove ball 1 at the fist time step and ball 2 at the second time step and…”
No. She said to remove 10. Then 20. Then 30. Etc.
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.
You like paradoxes and I think that contagious cause I have started thinking about paradoxes.
Should I drop RUclips premium and get curiosity stream?
Streaming is the paradox of cable.
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 :-)
Not a philosopher. Not a physicist. I live on the street and I'm very happy. I remember realizing that all things in the universe are on the cusp of two infinities. The infinitely small and the infinitely large. So there you are. Another paradox. And Jade, can't afford Nebula but love you on RUclips
How log table is created?(plz, make a video on this topic)
I love the concept of infinity. It has fascinated me for years now. I really really hope scientists will discover new facets of it still during my lifetime so I too may know of them while I'm around. I wonder how infinity would work in a math system that isn't based on counting, but something else.
This channel deserves more view