The Simplest Math Problem No One Can Solve - Collatz Conjecture

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The Collatz Conjecture is the simplest math problem no one can solve - it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via brilliant.org/veritasium get 20% off a yearly subscription.

Special thanks to Prof. Alex Kontorovich for introducing us to this topic, filming the interview, and consulting on the script and earlier drafts of this video.

Lagarias, J. C. (2006). The 3x+ 1 problem: An annotated bibliography, II (2000-2009). arXiv preprint math/0608208. - ve42.co/Lagarias2006

Lagarias, J. C. (2003). The 3x+ 1 problem: An annotated bibliography (1963-1999). The ultimate challenge: the 3x, 1, 267-341. - ve42.co/Lagarias2003

Tao, T (2020). The Notorious Collatz Conjecture - ve42.co/Tao2020

A. Kontorovich and Y. Sinai, Structure Theorem for (d,g,h)-Maps, Bulletin of the Brazilian Mathematical Society, New Series 33(2), 2002, pp. 213-224.

A. Kontorovich and S. Miller Benford's Law, values of L-functions and the 3x+1 Problem, Acta Arithmetica 120 (2005), 269-297.

A. Kontorovich and J. Lagarias Stochastic Models for the 3x + 1 and 5x + 1 Problems, in "The Ultimate Challenge: The 3x+1 Problem," AMS 2010.

Tao, T. (2019). Almost all orbits of the Collatz map attain almost bounded values. arXiv preprint arXiv:1909.03562. - ve42.co/Tao2019

Conway, J. H. (1987). Fractran: A simple universal programming language for arithmetic. In Open problems in Communication and Computation (pp. 4-26). Springer, New York, NY. - ve42.co/Conway1987

The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.13.1) [Computer software]. www.manim.community/

Special thanks to Patreon supporters: Alvaro Naranjo, Burt Humburg, Blake Byers, Dumky, Mike Tung, Evgeny Skvortsov, Meekay, Ismail Öncü Usta, Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal

Written by Derek Muller, Alex Kontorovich and Petr Lebedev
Animation by Iván Tello, Jonny Hyman, Jesús Enrique Rascón and Mike Radjabov
Filmed by Derek Muller and Emily Zhang
Edited by Derek Muller
SFX by Shaun Clifford
Additional video supplied by Getty Images
Produced by Derek Muller, Petr Lebedev and Emily Zhang

3d Coral by Vasilis Triantafyllou and Niklas Rosenstein - ve42.co/3DCoral
Coral visualisation by Algoritmarte - ve42.co/Coral



29 Tem 2021




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Pranav Pandey
Pranav Pandey 7 aylar önce
Your way of Explaining through Graphics is beautiful sir.
Anuj Agrawal
Anuj Agrawal 9 gün önce
wanna work on that
icebreaker900 14 gün önce
henry 370z
henry 370z 18 gün önce
Mathematician was correct waste of time
Ian Horler
Ian Horler 6 aylar önce
Eray X
Eray X 24 gün önce
Hahaha the part 12:34 where he shows himself while saying "One of the worlds greatest living mathematicians..." and then showing Terry Tao, was a funny little touch :D Appreciated.
Ragnar Odinsson
Ragnar Odinsson 2 gün önce
The birds and cats know math long before human added language to math to feel special.
Patrick Cooper
Patrick Cooper Aylar önce
As someone who goes to Syracuse university, totally caught me off guard when you mentioned it’s also known as the Syracuse problem. But I was more shocked it wasn’t a coincidence, looks like the math department here has spent a bit of time on the problem and picked up the name. I think they’ve given up on the problem because I hadn’t heard of it lol
Ragnar Odinsson
Ragnar Odinsson 2 gün önce
Dogs, cats, birds use math without much in the way of a mathematical language and some are much better at it then others, some cats take forever on deciding on a jump other do it without even slowing down and always land on the target location and some house cat breeds are much better at this then others. small slender cats with long bodies and large hind legs for jumping and are very good at turning their bodies in mid air to grab prey and birds on the way down, the better hunters take their time and push their hind legs into the ground and hold still trying to remain hidden until the prey looks away and before the jump some cats eyes change color a result of the cats night vision that could be a result of the amount of concentration used by the cat. man tries to turn everything into a language. animal can even figure out what some human sounds mean without repeating such sounds, a common one is the word for food, cats can learn what certain signs mean. a petting gesture can turn into a meaning, make the gesture and some cats will stop and decide if she or he wants to be petted, you can use a gesture for the word food and some cats will walk over to their dish, some cats know the game fetch but will refuse to play when dogs , cats even when other human are around and unlike dogs always seem to place the toy right in the center of the hand. the cat version normally means knocking the object around then grabbing it and bringing it back and placing in the center of the hand for the next toss and may even end the game by mocking a dog by laying down like a dog and sticking its tongue out. Cats love to observe and the amusing thing is cats sometimes attempt to teach humans.
Paige Rasmussen
Paige Rasmussen 4 gün önce
So we're not just a drinking school with a football problem but a math school with a drinking problem?
Robinson Cruise
Robinson Cruise 9 gün önce
@Woos cuz its something important he had no idea was going on in his university
icebreaker900 14 gün önce
monarchatto 20 gün önce
@Woos wtf is this comment lmao
John Hirano
John Hirano Gün önce
There’s actually a simple way to prove that a divergent series can be balanced by a convergent series due to the combined functions, but it’s too much of a hassle to explain. 3x+1 always is an even number, /2 is only 1/2 odd of the time. By nature you can’t assign a limit to a non-converting series so the true answer is to ignore the givens, but apply a limit to the results using probability, and you’ll get a nice tidy converging answer.
Infinity Plus 1
Infinity Plus 1 6 gün önce
The more I know about math and science, the more I realize how much we don’t know
Cosmic Nomad
Cosmic Nomad 5 aylar önce
I absolutely love how mathematicians always find the most random things to debate over!
Renyx Ghoul & God Slayer
As it is chaotic in nature, stubborn and inquisitive = mathematicians
Ricardo Affonso
Ricardo Affonso 19 gün önce
@Christ Loen the solution in itself is worth it. math is art, after all.
Adrian Ciobotaru
Adrian Ciobotaru 22 gün önce
this video is not about mathematics...
The Fishy channel
The Fishy channel 23 gün önce
@Orezio Pancrazio There are different types of people in this world. Some may love to do theory like me. I am a mathematician turned to pharmacy. I love modeling diffusion of particles. Its fascinating. Can you imagine being a pharmacy major and talking about math? Some people spend their whole life in way of religion. Some in the way of dancing, art. Its only a dead end until someone opens it. When looking for oil in the US, everyone thought its a dead end until Drake first found oil. everyone else had left. thats why he won. Always invest time in hard and dead end things cause thats where opportunity lies
W French
W French 27 gün önce
@Conner blalock I like to think someone somewhere on TRvid has commented THE counter example but we will never find it amongst the trolls
STEREO Freq 21 gün önce
Someone should try graphing the relationships between the digital roots of the target numbers. The thing I noticed right off is that in the base 10 system (0 - 9), the "+1" in the algorithm never allows the target numbers to have a digital root of 3, 6, or 9. I.E. if you start with 7 (putting the digital roots in parenthesis), it would look like this: 7(7) - 11 (2) - 17 (8) - 13 (4) - 5 (5) - 1(1) If you were to start with a 3, 6, or 9, the "+1" will force the digital roots back into the list of [1, 2, 4, 5, 7, 8] 3(3) - 5(5) - 1(1) A similar type of pattern emerges when you look at the digital roots of doubled-numbers. For example, if you start with any number other than 3, 6, or 9, and double it, then get the digital root, you'll never get 3, 6, or 9, but if you start with 3, or 6 you'll only get 3's & 6's and starting with a 9 you only get 9's. 1(1) - 2(2) - 4(4) - 8(8) - 16(7) - 32(5) - 64(1) and the pattern repeats 128(2) - 256(4) - 512(8) - 1024(7) - 2048(5) - 4096(1) etc. You'll notice in this sequence in particular, you once again have a 1, 2, 4 relationship with regard to the digital roots, in that the sequence goes: +1, +2, +4, -1, -2, -4 vs. 3(3) - 6(6) - 12(3) - 24(6) - 48(3) - 96(6) etc. vs. 9(9) - 18(9) - 36(9) - 72(9) etc. So, because the even numbers are always divided evenly and the odd numbers are always made even, it always pulls the digital root trend into [1, 2, 4, 5, 7, 8]. In cymatics, frequencies that have digital roots of 3, 6, or 9 generate standing waves. Adding or subtracting a hert will make the nodes travel forward or backward. It's hard to say how, but I think this is all related to how these numbers trend, because even if you start with multiple digit number that has a digital root of 3, 6, or 9, the next action will make its digital root a value of "1" before dividing by 2, which makes the next digital root 5, every time. In example: if we start with 15, which has a digital root of 6, then 15 x 3 + 1 = 46 (digital root of 1) / 2 = 23(5); if we start with 27, which has a digital root of 9, then 27 * 3 + 1 = 82 (digital root of 1) / 2 = 41(5); or let's try 417 which has a digital root of 3: 417 * 3 + 1 = 1252 (digital root of 1) / 2 = 626 (5) / 2 = 313(7) ...and you're back into the list of [1, 2, 4, 5, 7, 8] every time.
Jay Aich
Jay Aich 7 gün önce
This is super interesting, I also noticed something similar which is why I tried this equation using fractions. Example: 1.5 x 3 = 4.5 + 1 = 5.5 x 3 = 15.5 + 1 = 16.5 / 2 = 8.25…etc. The problem is that the .5 wasn’t changing much, so I decided that the rules apply to the .5, .7, .2, only. Example: 2.2 / 2 = 1.1 x 3 = 3.3 + 1 = 4.3 x 3 = 12.9 + 1 = 13.9 x 3 = 41.7 + 1 = 42.7 x 3…etc. This opened up a whole lot of opportunities and I did get close a few times, I also tried fractions like 13.568, but sadly even with the fractions I ended up in that same loop, it just took longer to get there.
Brian M
Brian M Aylar önce
Fascinating to see the correlation between the randomization of this equation and the patterns in nature and beyond, which should really be the focus in my opinion becasue the equation or problem itself doesn't seem to be a problem at all. I mean take replace 3 with 4 or with 5 and see what happens. There is always a pattern. It just so happens that the pattern of 3x+1 will always result in a sequence of dividing by 2 that will eventually overcome the multiplication of 3+1 reducing it to the 4-2-1 loop. I consider it solved, the solution which was presented in the video. Again, the real intriguing aspect is how that particular problem replicates randomness in nature, and well even other facets of this world including the stockmarket...hmmm..can anyone say matrix lol..perhaps this demonstrates that if you know the starting numerical value of anything, you can see how it will grow and perhaps when it will decline..ooops crazy conspiracy stuff leaking out now.That all being said, great job on the video!
Brian M
Brian M 27 gün önce
@Ian Allen Appreciate that. I find that many complex problems are easily solved through simplification and visualization.
Ian Allen
Ian Allen 27 gün önce
The problem, brian, is that an odd number can be expanded by 3/2 multiple times in succession. In fact, countably infinite number of times (that is to say, every bridge upwards is absolutely finite and eventually ends, but they grow infinitely long), and to make matters worse, you can go up a bridge, fall back some ways, and land on a second bridge that takes you even higher. And this pattern as well, repeats infinitely. But good on you, seeing that it is solved. Math is easy, when you aren't actually counting.
Osho Omniversity
Osho Omniversity 3 gün önce
Either it goes towards infinity or 0, to go to infinity, it always has to odd no, 3x + 1 can only be odd if x is even. Since adding 1 it makes impossible x to be odd always. Moment x is even, probability to go towards 0 increases. Lowest no is 2, so it is destined to fall in loop.
Raphat Aylar önce
What an amazing video. I have learned so much from just the side ways you took the explanation.
Dabo Life
Dabo Life 11 aylar önce
Math problem no one can solve: Exists Me: Finally I'm not the only one who is bad at math.
Lilliana Pabon
Lilliana Pabon Aylar önce
Azlan Adil
Azlan Adil Aylar önce
@Lilliana Pabon It was a true or false question. What do you mean 7?
Lilliana Pabon
Lilliana Pabon Aylar önce
I solved this question with google,THE ANSWER WAS 7
Azlan Adil
Azlan Adil Aylar önce
@The Reality Gab Umm… If you pick a number multiply it by 3 then add one if it’s odd, and divide it by 2 if it’s even. Will positive integers always end up in a 4,2,1 loop. Solve that.
Leopoldo Anaya
Leopoldo Anaya Aylar önce
Create animations with 3x+1
PsithyrosTV Gün önce
I wonder if there's any correlation between the base number (x) and the number of steps it takes to get to the 4, 2, 1 loop
Omgdodogamer 5 gün önce
15:33 i dont know if anyone else noticed this but the amount of perfect squares in each number roughly equals the sqaure root of that number. sqrt(100) = 10, sqrt(1000) = 31.6, sqrt(10000) = 100
Релёкс84 3 gün önce
@Omgdodogamer Yea you already said that. You formulated your conjecture, and I'm asking if you can prove it. I for one can, and it's a good exercice to try it yourself.
Omgdodogamer 3 gün önce
@Релёкс84 if you google perfect squares between 1 and 1 million it says 1000 and the square root of one million is 1000
Omgdodogamer 3 gün önce
@Релёкс84 15:33 "How many perfect squares are there in 100? 10." and the square root of 100 is 10. 1000? 31 and the square root is 31.6. 10000? 100 square root is 100
Релёкс84 4 gün önce
How strange... can you prove it?
furasoul93 27 gün önce
always when i hear about problems like this - easy to explain, hard to solve - i imagine some other dimensional species looking at us thinking "oh they're so close but yet so far away. why don't they look at this problem *this way*"
itisorisit Aylar önce
The problem "does the Collate Conjecture hold" is trivially decidable. The definition of "decidable" is (simplified) that it is possible to create a Turing machine that gives the correct answer. It is trivial to create a Turing machine that outputs "yes", as it is to create one that outputs "no". One of these machines gives the correct answer to the question. For decidability, we do not need to know which one. More generally, only problems with an infinite number of inputs can be undecidable, IF the conjecture is false. So the question "does 3x+1 terminate" may be undecidable, assuming both the answer "yes" and "no" occur for an infinite number of integers.
TheNordicNormie 9 aylar önce
Pretty much every subject in school is really interesting if I’m not forced to learn it
Guy 5 aylar önce
Pratana Kangsadal
Pratana Kangsadal 5 aylar önce
Victor Kappel
Victor Kappel 7 aylar önce
You just described the main problem with the current education system on several places on the world: They don’t make you interested in learning the subject, they force it down your troath
How the turn tables
How the turn tables 8 aylar önce
Quazi Rahman
Quazi Rahman 25 gün önce
For negative numbers, the equation should be 3x - 1, and you'll get the same results. (@ 15:04 min)
Levi Nevara
Levi Nevara 27 gün önce
You all should realize by now that 3x+1 will always point to an even number. If that number have prime number consisting of only 2, then it will get to 4-2-1 loop. So this equation will result an even number and the procedure is finding the number with all of its prime numbers consisting of only 2.
Ian Allen
Ian Allen 27 gün önce
This problem is beautiful and it touches on a vast number of fundamental concepts and outstanding conjectures. It is one of the greatest travesties of modern mathematics, that it is always introduced as "a dangerous problem that people are warned not to waste their time on." For shame.
Daniel Hed
Daniel Hed 24 gün önce
Im sure someone has tried this already but my first instinct to solve this would be to try to prove that all prime numbers terminate in 4,2,1. If all prime numbers do than that implies every number reduces to 4,2,1.
Tudor Iacob
Tudor Iacob 20 gün önce
@Max Muir what about odd numbers that aren't prime? edit to pe more clear. if you prove that all odd numbers reach 124, then even numbers do as well, which is probably what you are thinking about, but why do non-prime numbers always reach one of their divisors?
Max Muir
Max Muir 21 gün önce
@Joe Heitman eventually they will I could takes years for some numbers that are insanely big but yea they will and there is no other way for a loop to happen unless a prime number can be divided by 2 that isn't 2
Max Muir
Max Muir 21 gün önce
@R L all prime numbers are odd and all numbers dived by two will eventually be odd so if odd number can't loop then on 1 2 4 can
R L 21 gün önce
I'm wondering how you got the idea that this is true. I know it might be true, however at first glance, I don't know why it would be true. For example, if we know that it works for 3 and for 5, how do we know that it works for 15? Is there some pattern I missed?
R.P. McMurphy
R.P. McMurphy 21 gün önce
why would this lemma be true?
Diego de Paula
Diego de Paula 5 aylar önce
Whoever created all those graph animations is an absolute master in after effects expressions
Rubén Ossorio
Rubén Ossorio 18 gün önce
Logo l mmm yeah o lo
Abhishek Srivastava
Abhishek Srivastava 2 aylar önce
It's made by Manim, an animation tool created by 3blue1brown
IRON MANUAL 2 aylar önce
PotatoLord 2 aylar önce
I like men
Bob does art or something
@Jolly_Bells 990 did you watch the video?
Professional Butler
Professional Butler 13 gün önce
Didn’t watch the whole video, but I consider it more of a stats problem. There are infinite possible inputs, so many possible patterns, but think of it like this; while dividing and multiplying, odd multiplication adding 1 results in evens, but many evens when divided by two can create another even. So the initial function has a likelihood of increasing it, but as we test more and more numbers, the division by two takes control. Why? Because we’ve allowed it to divide multiple times by two when it is even. You have a 50/50 chance to get an even when you multiply and you also have a chance to get that when you divide. You will always multiply once, but there are many times you will divide more than once. Not sure the actual odds, but I can imagine it’s a back of the envelope formulation. This way I can imagine it’s more likely to eventually go down than up which will lead you to 1. Or you will just hit some power of two randomly along the way anyways, which technically if we run this an infinite number of times, we will at some point do it with any number and immediately get to 1. I think it’s a combination of those two things. I think that’s actually pretty intuitive.
J Modified
J Modified 12 gün önce
That does not mean there can't be a higher loop, or a sequence that increases indefinitely due to some currently unknown pattern. There are sequences that go far above their seeds.
Devanshi Singhal
Devanshi Singhal 4 gün önce
What do you think happens to decimal numbers when followed the colatz conjecture?
Brian Troy
Brian Troy 28 gün önce
Reading these comments, I'm seeing many people realizing that they number of steps remains consistent or close too consistent for many sizeable ranges of numbers. This is because of the tree that is the collatz conjecture in reverse. as in start at 1 and for each number you ever reach, choose to either multiply by 2 or sub one and multiply by three. This generates that cool looking tree they showed during the video. So those similar ranges are actually expected, because those values are simply at similar depths in that tree. What I've noticed that I think is more useful is the power of 0 in these sequences. If you only look at the last digit, 0 is your best case. it makes you /2 and will be either 5 or 0 again. but its that ability to recursively hit 0 that gets you some large drops in the value no matter how high you started. Also there are some "core branches" that show up more often than others. Obviously there's 2^x, but also (2^x)*10. which makes me wonder, could you prove that any number ending in 0 must converge? because if you can do that, you get 1-9 for free since that's doable even just by hand.
OrangeKnight420 2 gün önce
Yeah it’s unsolvable. And if there is a number out there we’ll probably be extinct before we find it. Also regarding the negative version of it and why it’s different, that’s like the easiest question ever. The +1 acts as a -1 in the negatives so the number goes down rather than up, making it significantly different
ParkieL 11 aylar önce
Oh my god, this poor animator. That is a serious amount of dedication. Looks fantastic!
Kalliboy 3 aylar önce
@Mehtab Traveller Maybe I'll work with this someday Python fascinates me everyday
NotYayaNguyen 3 aylar önce
@Good Nintendo player how do u know it’s a “he”
Llama Man
Llama Man 4 aylar önce
@Lucky The Luckless Wolf I know I am
Lucky The Luckless Wolf
@Llama Man no, you're amazing
Good Nintendo player
Good Nintendo player 4 aylar önce
He needs to be paid every single day $100,000 heh
Balam Jimenez
Balam Jimenez 10 gün önce
It was an amazing video, thank you. I am not a mathematician at all but I do have an observation/question/thought. Maybe the answer is not within the problem but outside the problem. This might just be babbling and outrageous so pardon my ignorance. Has anyone tried to develop the same problem for numbers in different bases? Like Sexagesimal numbers? The hypothesis would be that there is a number or series of numbers that are shared among Collatz conjectures of different bases. Of course it is unlikely all bases have the same Collatz conjecture model (3N +1 for odd numbers and divided by 2 for even numbers). I guess each base has its own Collatz conjecture model and that needs to be found first. So, after finding each base model, could be possible to find those numbers that are shared among conjectures. One or more of those shared numbers could be subject of a different loop than 4-2-1 in the base 10 Collatz conjecture. Probably the interaction of those numbers could create a unique loop different from each conjecture or a different unique tree that is not constrained by the base of the numbers used, and has its own behavior. What are your thoughts?
Tomas 10 gün önce
Well, the problem doesn't depend on the basis used, so it doesn't matter which basis we use. The only thing that matters is whether a number is odd or even
Rich Millich
Rich Millich 20 gün önce
I like to say that "mathematics is most often about the relationship between numbers and sets of numbers, not in computing anything." All too often we concentrate on utilitarian number crunching, which is boring, and why most students loathe math. Instead, patterns OF numbers and within sets of numbers are much more pleasing to the pattern making instincts of the human brain. Odd. Even. Positive. Negative. Fractions. Now here come the irrational numbers. Pi. Euler's Number. Phi, the Golden Ratio. Now here's a Cartesian plane. A unit circle. Sine waves, which we see and know in nature. Now here's a sphere. A hypercube. Fractals like the Mandelbrot Set. Procedures built with numbers that generate landscapes. Layers of infinity and an infinite number OF infinities, many of which we will never know. And somehow, within many of these mathematical constructs, we discover similar patterns over and over. Sometimes it feels as if there is a great unified system of patterns that revolve around each other, forming shapes, galaxies, anything we can imagine. THAT makes math beautiful. If we only taught it this way.
Elliot Alderson
Elliot Alderson 29 gün önce
Graphics is fascinating. Thanks for all the hard work.
Peaky2018 10 gün önce
Thankyou for putting in the effort to make this video I actually found it really interesting
shadyceddy 8 aylar önce
Fun fact: We are not mathematicians but we got interested by this.
A1 AR1
A1 AR1 18 gün önce
I somehow get curious enough to open these videos but by halfway thru I’m so lost it’s a waste of time for me to keep going. 😵‍💫😵‍💫. Yes, I have a college degree, studied physics, algebra etc but never got not into math enuff to follow this stuff.
golden rules
golden rules 20 gün önce
We want not look stupid .. but here we are 😭
Paolo 22 gün önce
@Amir Pakravan A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems
Paolo 22 gün önce
Fun fact: We are not mathematicians but youtube recommended us this video
Xogroroth666 25 gün önce
@iamDeano91 No, the answer is the sequence 4, 2, 1 :S
Santumi 26 gün önce
If you can make every single positive integer out of a combination of 4s, 2s and 1s, then every number can be reduced to that loop. There's no number that can't be made out of 4s, 2s and 1s
Brodie Eaton
Brodie Eaton 23 gün önce
15:52 completely unrelated note, did anyone else notice the parabola appearing on the graph? It makes sense for one to appear since it's graphing perfect squares, but I still find that kinda cool
Fred Lane
Fred Lane 19 gün önce
Although this may be of no value, it occurred to me that there is no upper limit of numbers, but there is a lower limit (the number 1). If there was no lower limit, the calculation would go in forever. The lower limit is the reason it stops.
Riguor 987
Riguor 987 Aylar önce
So here's something interesting: if you can just prove that for all numbers >1, each number will eventually go to a number less than the starting one, you'll prove the hypothesis.
The Musical Stylings of Brent Bunn
Mad respect to the animators here. That must've been a lot of work.
braum leon
braum leon 5 aylar önce
i wonder if there an effective way to animate like this, or we just do it manually?
Pratana Kangsadal
Pratana Kangsadal 5 aylar önce
Häherfeder 7 aylar önce
cisse de clercq
cisse de clercq 10 aylar önce
we do or best.
Matthew Gale
Matthew Gale 26 gün önce
I absolutely loved it you did have some divergent moments..... Don't let dark chocolate confuse you of it not being chocolate.... That's where some of your scientific arithmetics hit the wall
Zach 5 gün önce
I think things like this are pretty arbitrary bc the person who came up with "Do this for odd and do this for even" seemingly had no reason to set the equation as they did. It could have easily been Odd: 3x+1, Even: /2+1, or Even /2-1. ... Thus, a problem like this does not seem to have value to me.
Tyler Raffety
Tyler Raffety Aylar önce
After watching this, I feel like this 3x+1 to an odd number and x/2 to an even number is just a cycle to get every starting positive integer to a number on the 2^x line, which 1-2-4 is the start of (2^0=1, 2^1=2, 2^2=4, etc.), and because 3x+1 will always make an odd number even, and x/2 will always, eventually, make an even number odd (with the end goal being the odd number 1 that only lays at the end of the 2^x line), I feel like every positive number will end at the 4-2-1 loop
Bryan Lee
Bryan Lee Aylar önce
feel like i d never ever use this knowledge but it feel so good to learn so much!
Demens Clay
Demens Clay Aylar önce
A big shoutout ot the graphics department for making this 100% more understandable!
icebreaker900 14 gün önce
Lance Dela Torre
Lance Dela Torre 22 gün önce
Yet I still can't understand
Jdogg4089 23 gün önce
@Gvko A big shout-out to you who couldn't be bothered to proofread!
Anndy Arguedo
Anndy Arguedo 25 gün önce
Anndy Arguedo
Anndy Arguedo 25 gün önce
Ah yes, 999 likes
acire08 2 gün önce
just imagine like, a 12 year old, just... finding the answer in 2 seconds, and questioning how nobody could figure it out before them.
Farzana Riyaz
Farzana Riyaz Aylar önce
A googolplex (10^10^100) is far bigger than a millinillion (10^3003). I also think I can prove that 1 Millinillion is clearly a Type 2 -illion and that (10^10^3003) is familiarly known as 'Maximusmillinillion' or 'Millinillionplexed'
Ziva Meyer
Ziva Meyer 18 gün önce
Also makes me think of the warp drive problem where they realize when they factor in the universe is moving not just them suddenly the answer appears … what if we are missing a understanding of mathematics or life if self that would lend the poof or disproof or even better what if quantum level understanding possibly leads to a duality (granted my understand )(and I failed high math,)) is that I don’t see how it might apppy) We often find what we were so sure gets disproven sometimes totally by mistake or trying to prove or disprove something else The final answer to this I am sure won’t be the expected source or way of getting it
Bhagwat Kumar
Bhagwat Kumar Aylar önce
According to me most of the time when we add 1 in 3x there is one time the number which we will obtain as even will be a factor of two. So i think if you want it to be infinity then start with infinity. Because if you start with any number it will eventually get to 1 until it's decimal or irrational.
runciter naki
runciter naki Aylar önce
you had it there, the answer, for a brief moment near the end of your paragraph, then poof - gone
Marco Kapusta
Marco Kapusta 11 aylar önce
This math problem is actually like my trading portfolio, I can start with any number but end at $ 1
runciter naki
runciter naki Aylar önce
you posted the solution in your post there^ - hint; single character
DoYouLikeOculus 4 aylar önce
Then start at 0
Crasho 5 aylar önce
@Luca Disgusting Light Mode
Marco Kapusta
Marco Kapusta 5 aylar önce
@Anonymous000 I love it when a plan comes together
Anonymous000 5 aylar önce
Bruh I thought there was a hair on my pnor
JuggyBob 23 gün önce
The animations that Veritasium uses makes every video more complex than what it seems.
nonyabusiness 6 gün önce
We all got trolled by Collatz Dude said "Any number except 1 or 0" and literally had people busting their brains over it for decades
FOS Aylar önce
One thing interesting when I try it is that when the num is 2^¹⁰⁰⁰ , leave it running for 30 minutes and almost all of the number took 7248 steps, some are 7249/7229, others 7428. It seems like it can't go further than that for some unknown reason
Matthijs van Duin
Matthijs van Duin 29 gün önce
It seems in general that when you test numbers in some relatively range, the number of steps tends to be from a very small selection, e.g. testing the numbers M+1 through M+1000 for various M gives the following numbers of steps: M=2^1000: 7248 (97.0%), 7429 (3.0%) M=2^1001: 7249 (93.6%), 7430 (6.4%) M=2^1002: 7250 (89.7%), 7431 (10.3%) M=2^1100: 8121 (51.5%), 7428 (48.5%) M=2^1200: 9087 (100.0%) M=2^2000: 14726 (67.3%), 15243 (18.6%), 13157 (14.1%) M=3^630: 7854 (50.0%), 6652 (48.7%), 7642 (1.3%) M=3^631: 6651 (62.6%), 7853 (35.0%), 7641 (2.4%) M=3^757: 8001 (95.2%), 8973 (4.8%) M=3^1262: 14553 (99.5%), 13320 (0.5%) M=5^861: 14490 (95.9%), 14322 (4.1%) and just to make sure this also happens with "random" numbers rather than ones that are a prime power: M=round(Pi*2^2000): 13810 (82.6%), 15118 (17.4%)
runciter naki
runciter naki Aylar önce
your process is not the fallible part
Sooraj ____
Sooraj ____ 4 gün önce
Fun fact: there is a closed loop for 5 if we subtract 1 instead of adding
Agentkp 8 aylar önce
Mathematicians: Dont waste your time on this problem 20.7 million people: YES
Liam Wilson
Liam Wilson Aylar önce
@Frank Chary imagine if we do figure out warp technology and they actually call it warp technology lol
soobin doll
soobin doll 2 aylar önce
Abhijeet 3 aylar önce
Search about Abhijeetbyte Collatz Conjecture GitHub 😎🤣🤣👍👍..... Can't share Links on TRvid comments
Frank Chary
Frank Chary 5 aylar önce
We need to work on practical problems that solve mankind's various problems such as air water and ground pollution, developing cleaner energy, food water and resource supply and more equitable distribution. Having solved these problems then we can move on to developing Warp technology to open up the final frontier.
Baris Can
Baris Can 23 gün önce
It's a simple mathematical formula that can be explained similarly to entropy. I cant wait for humans to solve this one haha.
Richard Green
Richard Green 24 gün önce
In binary: 3x+1 is left shift (2x) and then add x (2x+1x) = 3x ... and then, if the result is all ones, when you add 1 the ones will cascade and you will get a power of 2 ... and that will go to the 4 2 1 loop. But most of the time, 3x will have some zeroes to prevent that cascade from happening. Dividing by two, in binary, is right-shift ... since the number was even, this eliminates the right-most zero.
John Budweiser
John Budweiser 23 gün önce
the reason there are different loops on the negative number line is because you're practically changing the function when x is a negative value, because you do the equivalent of 3x-1 instead of 3x+1
Terry Armbruster
Terry Armbruster Aylar önce
To continue. Since f can be rewritten in New form and can be generated as said as well as the other combos then by setting f and others in a matrix form we have the necessary requirements to map on into another. Or simply put prove x+1 and x-1 then 3x+1 is a simple spectral matrix manipulation. No trees or b's required.
Walkastray 11 aylar önce
A couple of days ago he had a poll on what colour would evens and odds would be if they had a colour. The poll decided blue as even and red as odd. In this video, he has the evens as blues and the odds as reds. I love how much he cares about his community and the little details.
Pratana Kangsadal
Pratana Kangsadal 5 aylar önce
Maria Maria
Maria Maria 5 aylar önce
@Tyler Lawrence I do. My favorite number since I was a child was 7. When I learned to read I played a game in my head when I was little. I liked the words with odd letters because I would divide them in my head . Odd numbered words would have an even number on the left and right and an odd number in the middle. I liked to spell them backwards and speak backwards when I was bored. I liked it much better than the even numbered words.
IrokoSalei 6 aylar önce
Is a multiple of 2 : Kalm Is another number : REAL SH T
Uloola 7 aylar önce
@Jim Balter Odd is right.
Uncle Exodus
Uncle Exodus Aylar önce
15:05 I like to think of zero as a mirror between negative and positive numbers, and multiplication and division reflect nicely, but addition and subtraction are more lateral, you could say, so they don't reflect. So can there be a formula that results in the same 4-2-1 loop on the negative side, instead of 3x+1 and dividing by 2?
runciter naki
runciter naki Aylar önce
you posted the actual/only answer in your post 3 times. Hint; single character
DisProfundis Aylar önce
Mark M
Mark M 23 gün önce
I think the reason why it seems impossible is because in this case, the number system is not defined as true infinity such that when a number is reduced to 4,2,1 it has nowhere to go into the spectrum of negative numbers. You can't say it's true for the number system when you only use an abstraction of the system. In fact, the equation itself puts a limit on the bounds of x. Further, we have integers that, albeit we call them even or odd, they act as both. For example, 10 is an "even" number but divided by 2, we get an odd. 2 is an even number, but divided by 2, we get an odd. 6 is even, but 6/2 is odd. That's a third of the base 10 loop that is our number system. Naturally, 4 2 1 are the least positive integers that fit the conjecture, so of course it will always amount to those 3 numbers given an unfair advantage of more even numbers available to divide. In other words, there are not truly the same number of odds and evens in the number system. This is also why 2 is even but still a prime..because it divides into an odd number and has nowhere to go by the limit defined by our number system that says it can't cross over to negative numbers. Think about all the other loops of 10 in the number system. They have somewhere to go when they're divided, until they get to the original single digits, they can't go below 0. Now, think of (ie) a base 2 number system. You don't see any other tiers of the loop, just 0,1,0,1,0,1 etc. Do you have the same problem with this conjecture in a base 2 number system? Probably not, but it would be interesting to see the results. My point is, we created the impossibility because our number system is flawed by our own definition of the actual base (0-9) versus its corresponding loops which are allowed to not follow the rules of said base. Further, if it wasn't flawed, infinity would be defined by an infinite number of positive and negative base 10 loops, not just infinite "numbers". I mean really, negative numbers, by that supposition shouldn't even exist. What we have is a 'base infinity' system that has no loop. That's my take on it anyway.
Max Muir
Max Muir 21 gün önce
We can solve it the loop it impossible to happen appstore from 1 2 4 becuse all prime numbers except from 2 can't be devided by two and when two dose it gets multiplied to a multiple of its self no other number dose apart from 2 and is the only number that can be a loop
There is a price to everything
Numerical gravity is honestly the best description for the pattern in this equation.
Tigre MC
Tigre MC Aylar önce
If you use any multiple integer number of all three variables you get a different number pattern that still repeats, even if you use different multiples. Edit: The pattern can have a different length too.
KūGëlßlitZ 11 aylar önce
i wrote this comment to appreciate that those graphs were not just random. There were exact and to the scale.
Pratana Kangsadal
Pratana Kangsadal 5 aylar önce
Artificial intelligence plus lottery
Found the mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
Rich bob
Rich bob 10 aylar önce
exact and to scale? The 'coral' ones were all textured, coloured and shaped in editing (not to scale at all) and the others are just basic graphs anyone could make in ten minutes on powerpoint ffs. If it was exact and to scale we would be looking at a black and white mess of straight lines. The graphs are mostly to look pretty.
T H A N A T O S 11 aylar önce
@Anastasia O I don't think anyone is wrong, we're all correct and absolute. We are all Human and have our flaws and talents... yet we will never come together to realize our true purpose once we step inside the classroom of thank you for reading this entire comment and not getting anything out of it. Have a nice day.
Anastasia O
Anastasia O 11 aylar önce
@EpicVideos Okay, but the original comment was not on the animations. It was just on the actual graphs and making those graphs. You just don't want to be wrong here lol.
Morris Frayman
Morris Frayman 15 gün önce
Maybe someone has made this observation (I can't go through 69034 comments), but if you keep taking log of log of log you should pretty quickly get to a number less than 1 in which case your next log is in negative territory. Then you can't take another log unless you're OK with complex numbers. So that's not a good formula to work with.
Vihan Aylar önce
If you apply the function 3n-1 to the negative integers, it would only have one loop of -4,-2 and -1. Similarly, if you apply the 3n-1 function to the positive integers, there would be many independent loops found.
J Modified
J Modified Aylar önce
Not "many" - three, as far as we know.
Nick atnite
Nick atnite 4 gün önce
The reason 3x+1 is different using negative numbers is because when using negative numbers the + works like a - so it works like 3x-1
Dad Dadson
Dad Dadson 28 gün önce
What do you do with fractions to determine odd and even?
Jokes on You
Jokes on You 11 aylar önce
Teacher: Why did you not answer the questions on your test. Me: Because the Math is not ripe enough for me to answer these questions
UTU49 6 aylar önce
@Delaraam I love WOTH. My other favorites are MNT and FUOPH.
Delaraam 6 aylar önce
@UTU49 YESSSSS 😂😩😩😩im so happy you know her
UTU49 6 aylar önce
@Delaraam Shizuku? Is that you?
Delaraam 6 aylar önce
Ken Seehart
Ken Seehart Aylar önce
At first I didn't think this was very interesting because I was only thinking of the escape case (launching to infinity) as being intractable but seemingly true based on the Brownian motion argument. If we pretend the structure is stochastic, then we can argue that the probability of finding an escape case is zero. But the loop case is far more interesting because I don't see any reason why such loops wouldn't exist.
runciter naki
runciter naki Aylar önce
"Better to Remain Silent and Be Thought a Fool than to Speak and Remove All Doubt"
Kris Siregar
Kris Siregar 22 gün önce
How the mathmatician try to solve this Conjecture gives me encouragemet to all my trivia math problems. Thanks for this amazing video
Tamás Kalocsai
Tamás Kalocsai 20 gün önce
Hi! Being proud as a hungarian as you mentioned Pólya, Erdős... and others who aren't mentioned here like Neumann, Teller, Kemény... just one thing about the pronounciation of hungarian names: Erdos is written with this letter: O-->Ő which sound like the french vowel "oe" in the word oeuf.
Karoly VEGH
Karoly VEGH 8 gün önce
Now this was fascinating. Appreciate it.
Mr Scientific
Mr Scientific 11 aylar önce
Nice work Soviets. You got me.
runciter naki
runciter naki Aylar önce
you fell into the 'trap' by yourself. Please take all the credit. What is a 'soviet'?, Propaganda is significant;y older than your avatar's face looks
Artificial intelligence plus lottery
Found the mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
Surya Prakash
Surya Prakash 6 aylar önce
@Ali Akram wwwwwwwwwwwwww¹wà
Martina Omeara
Martina Omeara 6 aylar önce
It's 4X the X doesn't mean multiply
Sameenoobgaming 6 aylar önce
Thehh uhhhh got me
demotherapy Aylar önce
I looked at the thumbnail, and felt pretty confident that I can solve this. The next second I start laughing uncontrollably. Never have I ever laughed at my own stupidity like this.
runciter naki
runciter naki Aylar önce
excellent, A++ - I would hire you based on that statement alone
Zemnia 24 gün önce
I should become a teacher and tell my students as homework "using this method find a number that doesn't go down into a loop"
Michael Gohlke
Michael Gohlke Gün önce
Keep the rules the same Odd x3+1, even ÷2 Feed it negative numbers and some interesting stuff happens
Arnie Olaer
Arnie Olaer 10 gün önce
This is just a formula that once it hits its lowest form it loops back to itself. One of the key part to this formula is dividing by 2 this stops the number by growing infinitely. The role of the plus 1 is just so you can use the rule of dividing by 2 when the number hits uneven. The multiplication will only work on an even number like number 3 because if even number is used like number 2 the answer will always be even number which adding by 1 and dividing by 2 will not work. And also multipying by an even number like number 3 is the part that will take the equation for a ride because the answer can either be even or uneven, until it hits what I called the "looping family numbers". The looping numbers using ×3+1÷2 is 4, 2, 1 and it repeats from there, but 4 is half of 8 and is half of 16 and if you keep multiplying these numbers by 2 which is the opposite of it's dividing by 2 rule you'll end up with something like this 4, 8, 16, 32, 64, 128 and so on and this can go infinitely and this is what I call the "looping family numbers", now all the equation has to do is hit of of these numbers that when divided by 2 will take you right back to 4, 2, 1 looping numbers. The chance of hitting the "looping family numbers" using ×3+1 is not impossible thats why it always leads back to 4, 2, 1 loop, it might take a bit longer for some numbers to hit the "looping family numbers" but it's not impossible. You can have other looping equation that will have the same behaviour like ×3+3÷2 or ×5+1÷2, I've only tried these 2 looping equations as I've only known about this math problem a few hours ago.
DasSkelett 11 aylar önce
Your "one of the world's greatest living mathematicians" joke totally killed me.
Artificial intelligence plus lottery
Found the Mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
Karan 11 aylar önce
@dgcfgv vgb thanks
dgcfgv vgb
dgcfgv vgb 11 aylar önce
@jet what? I'm so confused lol
Sarath Sreedhar
Sarath Sreedhar 11 aylar önce
jet 11 aylar önce
Since Narak rythems with the english word ungramatmatically correct then that is correct.
ssybesma Aylar önce
I noticed that all the initial odd numbers arrived at by halving are prime numbers. I don't know if that matters. What does it mean for the 3x + 1 results to runaway into infinity? It means successive divisions by 2 would have to result in a steadily trending higher odd number that was never arrived at before, and which led to 4,2,1. If an odd number was arrived at during any previous division by 2, you're done...skip to the next number. We need much more powerful computers to test these gargantuan numbers. Proving this can lead to infinity seems exceedingly hard.
Adrian Cigher
Adrian Cigher Aylar önce
10:00 Oh... So the problem is to prove whether all numbers end up in the 4-1 loop or not. Got it! Guess that's what a conjecture is.
Gaurav Muthusamy
Gaurav Muthusamy Aylar önce
So Basically, you’ll eventually run into a power of 2, which will bring you down to 1. This can also work if you just do x+1 instead of doing 3x+1.
FOS Aylar önce
@Lorand Horvath I use stopwatch and obviously remember the time that I start to run it, The activity monitor in my laptop also show how long java has been using my CPU just for this loop, I couldn't really change anything in the program as it's already running, I simply make it so that it stopped and show an output when the number gets to one
Lorand Horvath
Lorand Horvath Aylar önce
@FOS You could implement some checkpoints to see where you're at, so you can estimate the time Is your code running blindly?
FOS Aylar önce
@Lorand Horvath Hei, if you're going to write a code about this, If possible, try 3^2378284 It has a million digit and when I put it into my program, it already takes 4 hours and it hasn't stop (hasn't hit one). I know it might be long because it's a very very big number, but in theory it only has 30 millions steps, my laptop could handle 1 millions steps in a minute just fine. So I'm really curious if I found something interesting here Edit, More than 7 hours and still going
Aleksander Karch
Aleksander Karch Aylar önce
@FOS Nothing in particular. Besides, there are other loops like that (seed 17 also has an unique loop, while some numbers seem to grow rapidly and then abruptly stop at around 10^16, not going higher. This might be another loop, although a very long one
FOS Aylar önce
@Aleksander Karch Do you know anything unique on why the second loop exist?
Deepak Aggarwal
Deepak Aggarwal Aylar önce
Brilliant as usual. Really humbled by the guest speaker when he said "nothing! we have achieved nothing!"
runciter naki
runciter naki Aylar önce
even nothing is something
Hanya manusia biasa.
Hanya manusia biasa. 8 aylar önce
Me : "That's interesting puzzle, maybe I can solve it" Me 22 minutes later : "oh."
The Rayven
The Rayven 8 aylar önce
@ItzCharmian fair enough...
Grzegorz Hordejuk
Grzegorz Hordejuk 8 aylar önce
1 instead of 0 on the scale
The Rayven
The Rayven 8 aylar önce
@ItzCharmian which means you *HAVEN'T* solved it... If you had solved it, you would be more than willing to publish your findings, to prove you solved the equation... However, your lack of willingness to prove you solved the equation, only proves that the equation has not been solved because there is no proof that the equation has been solved... So in reality, the equation remains unsolved...
The music King
The music King 8 aylar önce
@ItzCharmian what is it
runciter naki
runciter naki Aylar önce
to the people whom produced this video - bravo, I haven't ever had this much fun trying to help people, all in a few hours commenting on their comments and helping people is what I have done to survive for most of my life. I am 53
fast 27 gün önce
This is not a problem, this is an explanation to the nature.🙃
Putin 25 gün önce
If maths class was entertaining id be a 10/10 student in no time
Emma 12 gün önce
Interesting. I dont know if Im able to solve it, that is my wondering as well. Why say I can and afterwards the result wont be the right one.I ll watch tomorrow the rest of the video to see if my calculs fit in your response. Untill now 3x+1 shall be a linear function on xy ax...
Levy Chevy
Levy Chevy 9 aylar önce
My calculus professor just introduced this conjecture to us last week, and ever since then I've been shamelessly addicted to just bringing up a random number generator for a starting point and wasting away the hours.
Artificial intelligence plus lottery
Found the mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
DHRUV SHARMA 8 aylar önce
Same brooo
James Pronger
James Pronger 8 aylar önce
Blah blah blah more replys. "Think differently and simply"
Diego Castro
Diego Castro 8 aylar önce
Anime Fan Club
Anime Fan Club 8 aylar önce
You have a great teacher if they motivated you to spend hours on this!
beepbop 28 gün önce
7:57 the statistical model given is all the proof I needed.
raxyls 6 gün önce
just imagine if there was a full number that was neither odd or even.
Spencer Guffey
Spencer Guffey Aylar önce
3x + 1 mathematically explains the inevitable collapse of everything in existence.. whether it be civilizations, your vehicle, or the universe itself.
Absynnian 16 gün önce
I would be curious to see if a sufficiently powerful quantum computer would be able to solve the problem or at least test enough seed permutations to be able to state with statistical certainty that the theorem is true.
Saifuu Suri
Saifuu Suri 8 aylar önce
This problem makes all my life problems seem like child's play. Kinda like having existential dread when you realize how large the universe is.
ThePiratePeter 8 aylar önce
@Saifuu Suri There is nothing to comprehend, he was just saying random jargon.
TheKeller101 8 aylar önce
@Saifuu Suri it's a spam bot
Pink Lion Gaming
Pink Lion Gaming 8 aylar önce
I only have existential Dread when I realize how old the universe is
Saifuu Suri
Saifuu Suri 8 aylar önce
@Phoenix 𝙾𝚙𝚎𝚗 𝙼𝚢 PROFILE Gee thanks for copy pasting my comment. I was almost too lazy to scroll up and read it for myself.
Ellie Inglis
Ellie Inglis Aylar önce
Maybe the problem is that everyone is calling it 3x+1 when actually the active part of the problem is the divide by 2. The operation is attempting to get to 1 and every time it hits a roadblock of an odd number the 3x+1 resets it back to even to continue the operation dividing by 2 to get to 1
Mr. Man
Mr. Man Aylar önce
I made a Python script really quick to find out what number less than 100 billion has the most jumps. I had to pull the plug on it at 15,733,191 because it was just taking a really long time to evaluate. That number jumps 704 times until reaching 1. Here’s the script I made: highest_count = 0 for x in range(1,100000000000): temp_x = x counter = 0 while x != 1: if x%2 == 0: x /= 2 else: x = 3 * x + 1 counter += 1; if counter > highest_count: highest_count = counter print(temp_x,' jumps ', highest_count, ' times.')
Alejandro Z
Alejandro Z Aylar önce
This equation is ridiculous but maybe when it solved it will give us insight to something amazing.
Not a Snowflake
Not a Snowflake Aylar önce
I haven’t watched a second of this video. But the equation in the thumbnail (3x + 1), is mathematically impossible. X could equal any number able to comprehended by the human mind. So basically, X=INFINITY
Not a Snowflake
Not a Snowflake Aylar önce
@J Modified just to give my input. I’ll say up front that i probably have no business talking about math. I mean, hell, I failed algebra 1 this year so this isn’t my domain.
J Modified
J Modified Aylar önce
Why comment then? The expression in the thumbnail is just an informal name for the Collatz conjecture.
Christopher 8 aylar önce
I'm not a mathematician but found this fascinating enough to watch the entire video.
Anshu Neupane
Anshu Neupane 4 aylar önce
Artificial intelligence plus lottery
Found the mathematical phenomenon A very interesting channel - " Artificial Intelligence plus lottery".
Matthew 8 aylar önce
same lo
kpink gamer
kpink gamer 8 aylar önce
ThaKid Kane
ThaKid Kane 8 aylar önce
What was the answer I don’t go time to watch the video but it should be 3 if it’s not it’s wrong
Ficdich Gogl
Ficdich Gogl 3 gün önce
"Take any number!" - There it starts, the paradox.
lumiwi 13 gün önce
me: thinks of a possible solution also me: *perhaps i was the chosen one*
Prepared Survivalist
Prepared Survivalist 17 gün önce
I feel like it's just a characteristic of numerical and mathematical arrangements that doesn't have any overarching meaning or pattern. There is likely no number that won't eventually repeat the sequence.
John W
John W 27 gün önce
Fantastic video, excellent visualizations, (evidence for God imo), thank you
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