The Fascinating Tale of the Simplest Math Problem No One Can Solve

Science • Views: 19,684

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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 https://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.

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

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

Tao, T (2020). The Notorious Collatz Conjecture — https://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. — https://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. — https://ve42.co/Conway1987

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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 — https://ve42.co/3DCoral
Coral visualisation by Algoritmarte — https://ve42.co/Coral

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55 comments
1
Eclectic Cyborg  Jul 30, 2021 • 10:13:55am

Collatz Conjecture

For more info if you don’t have time to / aren’t able to watch the video.

2
Shiplord Kirel: Fan of USPS, Goodyear, and Oreo  Jul 30, 2021 • 10:15:51am
3
Anymouse 🌹🏡😷  Jul 30, 2021 • 10:16:33am

re: #321 wrenchwench

Kai can do it in a ‘huh’. Spelling it out is good, too.

re: #324 Wendell Zurkowitz ((slave to the waffle light))

KEEP YOUR GOVERNMENT HANDS OFF MY MEDICARE!!!

4
Charles Johnson  Jul 30, 2021 • 10:18:29am
5
Wendell Zurkowitz ((slave to the waffle light))  Jul 30, 2021 • 10:19:44am

What are there more of, points along the number line or subdivisions between points along the line…

1,2,3….etc

0.1, 0.2, 0.3…etc

It is my suspicion that there are more of the latter and the subjective reality of our minds is larger than the objective reality outside it.

But this is not founded on anything

6
Belafon  Jul 30, 2021 • 10:21:20am

re: #5 Wendell Zurkowitz ((slave to the waffle light))

What are there more of, points along the number line or subdivisions between points along the line…

1,2,3….etc

0.1, 0.2, 0.3…etc

It is my suspicion that there are more of the latter and the subjective reality of our minds is larger than the objective reality outside it.

But this is not founded on anything

Those two are equivalent.
The fact that you can write f(x) = .x means that they are the same size.

7
Anymouse 🌹🏡😷  Jul 30, 2021 • 10:24:28am

re: #320 Dr Lizardo

I had not heard that. I imagine other red states will likely follow suit very soon. Good thing the GOP isn’t in control at the national level, because if they were, they’d make it Federal law.

Montana Anti-Vaxx Law: ‘Religious Exemption’ For Masks But Not For ‘Not Letting Kids Die In Your Own Home’ (Wonkette)

Montana’s senate president lives across the street from Ms. Shoenkopf. She was notified by a state Department of Labor notification (because she has a Montana business).

He directly lied to her (thread of messages are in the article). She contacted an ACLU lawyer, and that lawyer noted that the state senate president did lie about what the law does.

8
Wendell Zurkowitz ((slave to the waffle light))  Jul 30, 2021 • 10:24:57am

re: #6 Belafon

Those two are equivalent.
The fact that you can write f(x) = .x means that they are the same size.

at some point you have to run out of numbers!!!

9
wrenchwench  Jul 30, 2021 • 10:25:38am

I was told there would be no math.

I should have known, the way everybody keeps saying ‘+1’.

10
Dopamine Fish  Jul 30, 2021 • 10:26:59am

re: #7 Anymouse 🌹🏡😷

I read the article. That Montana law is a floating dumpster fire. It is the purest example of conservative performance art bullshit currently in existence - yes, even over Ron DeathSantis’s (R-FL) coveted social media anti-cancel-culture law.

11
Belafon  Jul 30, 2021 • 10:28:53am

re: #8 Wendell Zurkowitz ((slave to the waffle light))

at some point you have to run out of numbers!!!

Cardinality (roughly the size) of an infinite set is an interesting subject. Mathematically, if you can find a reversible function from the counting numbers to the set you’re working with, then it’s the same size as that set. For instance, the set 0, 1, 2, 3… is the same size as 1, 2, 3, 4… because I can write f(x) = x-1. And for yours, all we have to is put a decimal in front.

12
wrenchwench  Jul 30, 2021 • 10:30:40am

re: #10 Dopamine Fish

I read the article. …

If LGF ever starts asking, ‘Would you like to read the article first?’ before every comment and upding, I don’t know what I’ll do.

13
Dopamine Fish  Jul 30, 2021 • 10:32:27am

re: #12 wrenchwench

If LGF ever starts asking, ‘Would you like to read the article first?’ before every comment and upding, I don’t know what I’ll do.

Don’t worry, this isn’t FARK. We don’t get into flame wars based on not reading the article, like a bunch of plebs.

14
Wendell Zurkowitz ((slave to the waffle light))  Jul 30, 2021 • 10:32:58am

re: #12 wrenchwench

If LGF ever starts asking, ‘Would you like to read the article first?’ before every comment and upding, I don’t know what I’ll do.

How about asking “Would you like to register to vote first?” before making any political comment

15
JOE 🥓  Jul 30, 2021 • 10:35:01am

Can’t handle math problems thanks to the 8th Grade Algebra Teacher From The Portal Of Hell.

Motherfather always ridiculed me, made fun of my Afro hair and my clothes. He loved screaming at me saying I was a failure.

Years later when I went back home for Mother’s funeral I was grocery shopping for my Dad. I ran into that prick and he started up right where he left off and I went into full Harlan Ellison Tongue Fu® mode and ripped a dozen assholes into him as I reminded that worthless piece of shit that I graduated college and got my MA in Economics even though he said I was a nobody and I would be a failure. I also let that SOB know that the so-called failure had an International Master rating in correspondence chess.

After I finished with the Tongue Fu® he looked like I plopped him into the Three Mile Island reactor.

It felt so GD glorious to release that after all the abuse he and his fellow “teachers” did to me

16
lawhawk  Jul 30, 2021 • 10:40:05am

re: #12 wrenchwench

If LGF ever starts asking, ‘Would you like to read the article first?’ before every comment and upding, I don’t know what I’ll do.

I see those prompts, and I’m reminded of …

“Would you like to know more?”

17
The Pie Overlord!  Jul 30, 2021 • 10:40:13am

WHOA

18
No Malarkey!  Jul 30, 2021 • 10:41:43am

These will leak as soon as Congress gets them!

19
Charles Johnson  Jul 30, 2021 • 10:42:13am
21
sagehen  Jul 30, 2021 • 10:47:39am

re: #18 No Malarkey!

These will leak as soon as Congress gets them!

What’s the over/under on how quick?

I’m betting 4 hours.

22
Dr Lizardo  Jul 30, 2021 • 10:48:53am

Trump right now…

World’s Biggest Fart - The Hippo

23
Anymouse 🌹🏡😷  Jul 30, 2021 • 10:50:37am

re: #326 Dangerman

i can only do the best i can do.
and i have choices others may not.
many businesses around here have posted their health policies - it steers business.
if someone wont mask up or display basic vigilance at my door, i wont ‘ban’ them.
just a simply, sorry, changed my mind, dont need the service.

Republicans are busy stripping the power of businesses to require masks at all (see Deth Santis for example). It might take years for a property rights case to make it to the Supreme Court, while they continue to push their democide.

In a mostly blue state, businesses which try to prohibit masks could be hurt by the market. In red states, they will be rewarded, and us liberals will be left to die (while people in blue states say we deserve it for voting in Republicans).

24
wrenchwench  Jul 30, 2021 • 10:51:19am

Save the Dinosaurs!

25
Dopamine Fish  Jul 30, 2021 • 10:52:06am

re: #21 sagehen

What’s the over/under on how quick?

I’m betting 4 hours.

For them to leak once Congress gets them? I’d take the under. 4 hours from now? Definitely WAY over. This is a Friday afternoon in the finest bureaucracy in the world. Congress won’t see those documents for at least a week.

26
Backwoods_Sleuth  Jul 30, 2021 • 10:52:37am

1GWTMDwgg3ffKciXqT4o6JBTZbvCc/1I10hguHnM5dyJzvAlN7duqC+DvMBvlaCUlh39Vwhe4RWobQ4FSIfJDNVxnrs48NX3tcOLol00Aa3dwgWTFE9PttMll8GMl5/JCdKxREbOOMo=

27
Dopamine Fish  Jul 30, 2021 • 10:53:09am

re: #26 Backwoods_Sleuth

[Embedded content]

0NGmbZqr6jyoBRannH/opclW7lo3TZ8COKkmT6qqls5/AsRGI9prXlsPqIg4SN4+UNn0/BKlAx3vmsVWXT7RsyTXJ0P2lKRy

28
JOE 🥓  Jul 30, 2021 • 10:53:23am

re: #18 No Malarkey!

These will leak as soon as Congress gets them!

[Embedded content]

WONDERFUL!

I want to see Mussoweeney’s head explode when his tax returns are leaked!

It’ll be right out of Cronenberg’s Scanners! 🥳

29
Dopamine Fish  Jul 30, 2021 • 10:54:42am

re: #28 JOE 🥓

WONDERFUL!

I want to see Mussoweeney’s head explode when his tax returns are leaked!

It’ll be right out of Cronenberg’s Scanners! 🥳

And you just KNOW that the CPAs of Twitter will be all over that shit as soon as it drops, to tell us all the ways in which he “creatively accounted” to get out of paying taxes, and how many of them are actually legal.

30
JOE 🥓  Jul 30, 2021 • 10:55:23am

re: #21 sagehen

What’s the over/under on how quick?

I’m betting 4 hours.

hell it won’t be even 4 milliseconds before the Post and Times get a hold of them!

31
Michele: Recovering Social Media Addict  Jul 30, 2021 • 10:55:46am

re: #26 Backwoods_Sleuth

[Embedded content]

RQlxdoew6smbf72EN7w3s2C2/cMz3TmGlRLxCfB1B7XQ5Nk/FWK7irY/yix2rg+63MdlTIyHabqYYLZBn5RWZw+wAwKNBcPWKLRWZq8Vrj8=

32
Dopamine Fish  Jul 30, 2021 • 10:56:14am

re: #30 JOE 🥓

hell it won’t be even 4 milliseconds before the Post and Times get a hold of them!

And the day the Times article drops will be a FNDT of EPIC proportions.

33
Dangerman  Jul 30, 2021 • 11:00:16am

re: #26 Backwoods_Sleuth

[Embedded content]

aHZQ8K50AY1sMukxjIv0tmjpAXHsMnXapCW2TJ22FLvIX1vWHdb3drml9uk1vcBsjkbWfqtLQJiLQ/FEaljD7wZiYFfgTOlUhpHw9Hex88vu0P6BKiGNGKQ9++OLWh0O

34
JOE 🥓  Jul 30, 2021 • 11:00:53am

Meanwhile at Mar-A-LARDO…

Trinity Test Latest HD Restoration

35
Dangerman  Jul 30, 2021 • 11:01:18am

re: #29 Dopamine Fish

And you just KNOW that the CPAs of Twitter will be all over that shit as soon as it drops, to tell us all the ways in which he “creatively accounted” to get out of paying taxes, and how many of them are actually legal.

I’ve been sharpening my knives and pencil points for several years

36
JOE 🥓  Jul 30, 2021 • 11:03:56am

re: #35 Dangerman

I’ve been sharpening my knives and pencil points for several years

And right now KKKevin McKKKarthy is hiding in the bathroom scared to death as the reporters are banging at the door!

37
Michele: Recovering Social Media Addict  Jul 30, 2021 • 11:04:45am

Later Lizards. I’ve been on long enough today. The meat world calls.

38
Dangerman  Jul 30, 2021 • 11:04:49am

39
Dangerman  Jul 30, 2021 • 11:06:01am

40
The Pie Overlord!  Jul 30, 2021 • 11:07:53am
41
No Malarkey!  Jul 30, 2021 • 11:09:37am

re: #23 Anymouse 🌹🏡😷

Republicans are busy stripping the power of businesses to require masks at all (see Deth Santis for example). It might take years for a property rights case to make it to the Supreme Court, while they continue to push their democide.

In a mostly blue state, businesses which try to prohibit masks could be hurt by the market. In red states, they will be rewarded, and us liberals will be left to die (while people in blue states say we deserve it for voting in Republicans).

We’re vaccinated. The Republicans will do most of the dying.

42
retired cynic  Jul 30, 2021 • 11:10:46am

A Colorful Macro Photo of Beach Sand Reveals Infinitesimal Fragments of Coral, Quartz, Shells, and Plastic
thisiscolossal.com

Amazing!

43
The Pie Overlord!  Jul 30, 2021 • 11:10:47am

re: #26 Backwoods_Sleuth

Z9oLKwWkltS6llzos8lS32iAY3MNCppl7ATgZwuCB8bBKl1N5jiPbzssxHN8Ugm6/81eaanrJysP018uzGN1T/rK+RyHnbU6

44
Charles Johnson  Jul 30, 2021 • 11:11:20am
45
wrenchwench  Jul 30, 2021 • 11:13:19am

re: #44 Charles Johnson

You beat Kai by one!

46
The Pie Overlord!  Jul 30, 2021 • 11:13:30am

re: #44 Charles Johnson

WHOO LOOK AT THAT RATIO!!!!

47
Dangerman  Jul 30, 2021 • 11:13:31am
48
Dopamine Fish  Jul 30, 2021 • 11:15:39am

re: #47 Dangerman

EXCUSE ME, AREN’T YOU SCIENTISTS ALWAYS THE ONES SAYING, “IT’S NOT THE FALL THAT KILLS YOU, IT’S THE SUDDEN STOP AT THE END”?!? I HAVE A RIGHT TO AUTO-DEFENESTRATE IF I WANT!!! *YEET*

49
Anymouse 🌹🏡😷  Jul 30, 2021 • 11:15:50am

re: #5 Wendell Zurkowitz ((slave to the waffle light))

What are there more of, points along the number line or subdivisions between points along the line…

1,2,3….etc

0.1, 0.2, 0.3…etc

It is my suspicion that there are more of the latter and the subjective reality of our minds is larger than the objective reality outside it.

But this is not founded on anything

There are objectively more tenths than units. However, both are ∞ in quantity.

50
Anymouse 🌹🏡😷  Jul 30, 2021 • 11:19:11am

re: #8 Wendell Zurkowitz ((slave to the waffle light))

at some point you have to run out of numbers!!!

That’s it boys, we’ve reached the end of the number line. It’s Miller time.

51
Eventual Carrion  Jul 30, 2021 • 11:26:20am

re: #22 Dr Lizardo

[Embedded content]

Trump right now…

[Embedded content]

Video

That was a massive shart

52
Anymouse 🌹🏡😷  Jul 30, 2021 • 11:26:53am

re: #26 Backwoods_Sleuth

9zTULmMDhvVQ4uBK+t86k5B5HBGdzn3d81x8RxeBWFFnpbURVJYil6kaK/OKTIr6

53
JOE 🥓  Jul 30, 2021 • 11:27:56am

re: #44 Charles Johnson

54
sagehen  Jul 30, 2021 • 11:42:45am

re: #53 JOE 🥓

When Medicare was under discussion, my dad (anesthesiologist) was opposed. The pay was lower than what Blue Cross or any of the other insurance companies paid, and he was concerned he might not get to choose between Medicare and non-Medicare patients.

By the end of the first year of its implementation, he LOVED it. The surgeons screened which patients would be on his schedule so they were still mostly private insurance, the sudden influx of happy happy grandchildren in the corridors during visiting hours improved his day, the gratitude of middle-class adults who were relieved of how to take care of their parents’ medical bills… plus Medicare pays REALLY QUICK and there’s no jumping through hoops to get approvals.

55
Florida Panhandler  Jul 30, 2021 • 3:03:04pm

re: #32 Dopamine Fish

And the day the Times article drops will be a FNDT of EPIC proportions.

Just a reminder that we are just 7 months having been relieved of the Trump nightmare. In this time a tremendous amount of damage has been undone or is being addressed- the insane EO’s, treaty undermining, slimy dept appointments and many other remnants from a sewer dumpster fire have already been washed away. Now we can start to address the actual person responsible by the same method used to send other Mafia types to prison- taxes.

Reading through my posts one could gather I am one to claim the imminent downfall of the US regardless of what is to come. This is not my feeling at all but I do believe we have just this one chance- sending a true monster and ALL of his crony hacks, connected family and assorted toadies to prison before it is too late. And that window is closing rapidly.


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