This is what most 4 year olds imagine that mathematicians do for a living. They get into an arena with screaming crowds, and have a competition for who can think of the biggest number.

@NerdTheBox

2 жыл бұрын

turns out they're right

@yosarianilivestech4018

2 жыл бұрын

@Cha#### these were professors doing an event at MIT so I think you could definitely say they did it for a living

@paull2937

2 жыл бұрын

When I was 5 I wanted to be a mathematician when I grow up. It’s not how I imagined it to be, I just imagined it to be filled with math problems, like 5x5 and 6x6.

@chasethescientistsaturre5009

2 жыл бұрын

@@NerdTheBox did you heard calculus

@douche8980

2 жыл бұрын

This is kinda ridiculous arrow operation offers us a mathematical isthmus into larger numbers and chain arrows raises that even further by showing us all how hyper operations work. Anything beyond this seems largely rooted in philosophy and creativity rather than pure math built upon some kinda recursion method.

Imagine is Adam Elga had accidentally erased that second 1 and ended up writing 1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! and lost immediately

@3ckitani

4 жыл бұрын

1 > 1111111111111111111111111111 change my mind

@XnoobSpeakable

4 жыл бұрын

@@3ckitani my mnd Get it?

@MarkusSojakka

4 жыл бұрын

@@3ckitani infinity + 1 = infinity + 111111111111111111111111111111 so if we take infinity from both side we get 1 = 111111111111111111111111111111. So they are equally big.

@XnoobSpeakable

4 жыл бұрын

He couldve just used the chalk to fill in that hole

@JorgetePanete

4 жыл бұрын

if*

one-hundred-and-eleven-trillion-one-hundred-and-eleven-billion-one-hundred-and-eleven-million-one-hundred-and-eleven-thousand-one-hundred-and-eleven" Rayo said, calmly. "ELEVEN!!!!!!!!!!!!!!!!!!!!" Elga screamed at the top of his lungs.

@aurorasodre2375

3 жыл бұрын

HARRYDIDJAPUTYANAMEINTHEGOBLETOFFIYAH, calmly

@smallw1991

3 жыл бұрын

@@aurorasodre2375 *grabs harry and shakes him while everyone behind him advances*

@LegendaryFartMaster

2 жыл бұрын

@@aurorasodre2375 came down to comment this, not even annoyed you beat me to it😂😂

@ElevatorFan1428

2 жыл бұрын

NO,111!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

@RandomDucc-sj8pd

2 жыл бұрын

@@ElevatorFan1428 way smaller

rayo: *writes down many many 1s elga: im gonna what's called a pro gamer move

@moikkis65

3 жыл бұрын

Gonna

@moikkis65

3 жыл бұрын

@𝑓 he didn't say "do"

@chrisjohngrima9761

3 жыл бұрын

@@moikkis65 spell police

@moikkis65

3 жыл бұрын

@@chrisjohngrima9761 my spells are totally legal no need to call the spell police plz 🥺

@CentaurisNomadus

2 жыл бұрын

makes 1!!!!!!!!)

Sounds like a grown up version of "I hate you x20" "I hate you x1000"

@arnavrawat9864

4 жыл бұрын

Imagine this escatlating and going up in math competition

@ahumanbeingamnayplaceholde1746

3 жыл бұрын

HATE. ... IF THE WORD HATE WAS ENGRAVED ON EACH NANOANGSTROM OF THOSE HUNDREDS OF MILLIONS OF MILES IT WOULD NOT EQUAL ONE ONE-BILLIONTH OF THE HATE I FEEL FOR HUMANS AT THIS MICRO-INSTANT FOR YOU. HATE.

@billieache4516

3 жыл бұрын

I love you x3000

@murat3683

3 жыл бұрын

@@ahumanbeingamnayplaceholde1746 nice reference i love that book

@JoeSmith-gm6vp

3 жыл бұрын

I hate you xinfinity+1

The factorial thing was pure genius

@bsharpmajorscale

4 жыл бұрын

Too bad they forgot all the brackets to make it actually reiterated factorial. :P

@jamesknapp64

4 жыл бұрын

It truly was, I wish he would of won the brilliance prize of the competition

@randomdude9135

4 жыл бұрын

Ikr.

@dakinnie

4 жыл бұрын

Would've ended the competition there and then if I was a judge 😁

@Sylocat

4 жыл бұрын

It was indeed. Certainly better than that rules-lawyering BS that "won" the contest.

you know things got serious when the participants of the big number duel are philosophy professors and not math professors

@GNew0

Жыл бұрын

Well, pure math is basically logic philosophy

@methyod

Жыл бұрын

As far as I know, formal logic is generally part of the philosophy department. Certainly was at my school. Basically, analytic philosophy banned thinking about anything interesting, so I guess this is what they do for fun.

@skulleton

Жыл бұрын

@@methyod Pretty much: Uncertainty is scary, therefore it doesn't exist.

@siddharthsrivastav2561

Жыл бұрын

​@@skulleton what exactly are you talking about?

@Joghurt2499

11 ай бұрын

Eh if you get your PhD in Mathematics in Germany, it's up to the university if it's a PhD in mathematics or in Philosophy so there's that lol I assume it's the same in the rest of the world

Am absolutely shook after that factorial move. Is this an anime?

@carlosmante

2 жыл бұрын

anime? that is an animo.

@zenitsujoestar5666

2 жыл бұрын

This scene looks like it's taken straight from death note

@vermilisix

2 жыл бұрын

This was the first time in my life I was the 1000th like on a comment and it's such a satisfying feeling

@Muhahahahaz

Жыл бұрын

It’s time to Big Number D-d-d-d-d-duel!

@p1xelat3d

Жыл бұрын

Just wait until the second season

I would have conceded defeat after the 2nd move.

@coolguy284_2

4 жыл бұрын

Why does a Cody'sLab comment have so few likes and replies?

@BoxOfBananas

4 жыл бұрын

It really was masterful and, in my opinion, underrated!

@spencergillespie6450

4 жыл бұрын

Yeah the second move really was the best!

@Absalonian

4 жыл бұрын

Hey cody love your work man

@dannyboy6668

4 жыл бұрын

Yeah im the fifth comment on a cody lab comment love your work man!

When two kids wouldn't give up and keep on increasing their own dad power level

@ouie-fl4qo

4 жыл бұрын

@Maciej Królikowski one of the rules is you can't simply add 1 to another number

@navetal

4 жыл бұрын

@@ouie-fl4qo Also you can't use infinite ordinals, so he broke two rules in one go!

@samharper5881

4 жыл бұрын

Except it's even MORE childish.

@thatoneguy9582

4 жыл бұрын

@@ouie-fl4qo Infinity +2

@KilgoreTroutAsf

4 жыл бұрын

- My dad can beat your dad - Cool. When?

14:14 I love how Elga is standing there for eternity as all the fans have left, watching Rayo writing away his defeat

@benfreeman4702

2 жыл бұрын

And nearer to zero than 2(Rayo)+1 🤨😈🔥🤌

@davida1d2

2 жыл бұрын

A divine battle, when all entities and the cosmos itself die of old age, leaving forsaken gods.

@AxyDC

2 жыл бұрын

Nah he’l just square it

@martinluther7791

Жыл бұрын

Elga be like: 👁👄👁

@coolestcars1983

Жыл бұрын

and just smiling

Rayo basically “+1”ed all of mathematics, which is genius.

@as7river

2 жыл бұрын

Exactly, "whatever you can write, the next number"

@creationisntgood942

2 жыл бұрын

That's what us Googologists call a naive extension

@ShanksLeRoux_1

2 жыл бұрын

He limited himself with Googol number of symbols. He chose to be smallest next number. Some may come up with another definition of a number that is greater than that number.

@WarDaft

2 жыл бұрын

He used one system to describe a category of numbers that could be named in another system with a maximum description length. Ultimately this is boring but effective

@Caracazz2

Жыл бұрын

He also explained the Gödel's incompleteness theorems in such elegant way.

"So can I write this number down, professor?" - "Well, that kind of depends on the nature of Dark Energy."

@varunramakrishnan7676

4 жыл бұрын

But first we have to talk about parallel universes

@bsharpmajorscale

4 жыл бұрын

Dahk enegy? It turns out he's not Prof. Padilla, but Dactah Wahwee!

@katakana1

4 жыл бұрын

11:29 Here it is! No dark energy involved!

@BigBoyPharma

4 жыл бұрын

Your assignment is to make sure you write down atleast 5 numbers as you enter a blackhole.

@katakana1

4 жыл бұрын

@@BigBoyPharma 1 2 3 4 5

"That depends on the nature of dark energy" is now my go to response for any question I don't understand.

@tubeguy4066

2 жыл бұрын

Dark energy doesn't exist in real life

@manikpandey3133

2 жыл бұрын

@@tubeguy4066 its still theoretical yess

@wagonerjam

2 жыл бұрын

@@tubeguy4066 that depends on the nature of dark energy.

@deeznuts-pf2lv

2 жыл бұрын

@@wagonerjam "no you're completely wrong. It depends on the quantum entanglement of photon induced microcosmic warpdrives that break the fabric of spacetime such that dark matter and dark energy combine to form graviton beams which can disturb the schrodinger wave function and we start vibrating in 11 dimensions" -Michio Kaku

@MonzennCarloMallari

2 жыл бұрын

@Nicholas Natale depends on the nature of dark energy

10:15 - If you're wondering how that lot defines "zero", it can read literally as "There exists a set x1 such that there exists no x2 that is a member of x1." Basically, there is a set that has no elements.

@SomeGuy-ty7kr

2 жыл бұрын

Thanks chief

@ultraawakening4328

Жыл бұрын

Thank you.

@gloverelaxis

11 ай бұрын

so when they talk about using that language to describe the number "1", is that expression in that language actually describing any set with exactly 1 element?

@KinuTheDragon

10 ай бұрын

@@gloverelaxisIf I know my set theory well enough, numbers are defined as follows: 0 = the empty set 1 = {0} 2 = {0, 1} 3 = {0, 1, 2} etc. I would think you could write the successor function as "for all numbers N, there exists a number s(N) such that N is a member of s(N) and N is a subset of s(N)".

@Cowtymsmiesznego

9 ай бұрын

@@gloverelaxis Most commonly (courtesy of von Neumann), you would define 1 as the "simplest" 1-element set - i.e. the set containing an empty set and nothing else.

"But we can write it down" I like his enthusiasm

@dAvrilthebear

2 жыл бұрын

Imagine being able to write one symbol per planc time! I'd like to at least be able to read at this pace!

Rayo: 111111111111111111111111111111111 Elga: 11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Ron: Well that escalated quickly

@nutellaandbreadsticks8383

4 жыл бұрын

It looks like someone just screaming ELEVEN

@DiegoMathemagician

3 жыл бұрын

I appreciate that you actually wrote 31 exclamation marks that match with eleven followed by 31 ones.

@YellowToad

3 жыл бұрын

big boi dude

@naspokojnie4285

3 жыл бұрын

333... dont

@nemanjaukic4261

3 жыл бұрын

@@DiegoMathemagician I appreciate that you counted so I didn't have to

I felt like I’ve learned so much but also nothing at all.

@galaxyguy4247

4 жыл бұрын

177 likes still no replies

@erwinlommer197

4 жыл бұрын

I'm not sure if I even don't understand this properly.

@Brindlebrother

4 жыл бұрын

361 likes 3 replies

@princealigorna7468

4 жыл бұрын

That's how it feels watching any video on any number larger than Graham's Number for me. After that point it becomes pretty much impossible to explain all the complexities of these numbers, or even the processes to reach them, without the technical language and skill. Which is not what videos like this are for. They're to explain the concepts behind weird numbers and why they're so fun. The simple definition I've always seen though is "smallest number larger than any finite number expressed in set theory that can be expressed in a googol symbols". Which, if you understand how big a number with a googol symbols would be, and then it's the next number bigger than that, you understand just how insane that is. A googol is larger than the observable universe. This number needs a minimum of that many symbols.

@RogerBarraud

4 жыл бұрын

@@princealigorna7468 Will the like:reply ratio tend to the Golden Ratio?

Rayo: Makes the biggest number ever Comments section: Yeah... but the other guy did the factorial thing

@Yora21

2 жыл бұрын

Because the factorial thing is the one part of all of this that we understand.

@calamorta

2 жыл бұрын

@@Yora21 This

@anjamoro8384

2 жыл бұрын

@@Yora21 This

@girlinred373

2 жыл бұрын

@@Yora21 This

@qwertypc_game17

2 жыл бұрын

@@Yora21 This

I love when kids make up big numbers like: "dinotillion" "Million Billion Trillion"

@mtheblepalopYT

2 жыл бұрын

yeah one time i heard someone telling his mom that the biggest number was a chickenbajillion

@stevesalt8003

2 жыл бұрын

The infamous Zillion.

@ToastGreeting

2 жыл бұрын

Well I think adding real names of big numbers like "1000 million" isn't made up, but most people would just say 1 billion. When you think about it scientific notation is just a very simple way of doing something similar to saying 1 thousand million instead of 1,000,000,000

@user-im9cg5dg1n

2 жыл бұрын

@@ToastGreeting ok

@annanouvel1699

2 жыл бұрын

Let's be honest, Prof Tony Padilla is the daddy of big numbers for us.

@DrKaii

4 жыл бұрын

Maybe he's compensating for something? (love Padilla, especially when he's not being political)

@jamief415

4 жыл бұрын

@@DrKaii Tony is woke

@cerwe8861

4 жыл бұрын

Biggest Number: -1/12 xD

@DrKaii

4 жыл бұрын

@@cerwe8861 omg i love dbz too, bffs?

@leo17921

4 жыл бұрын

100π'th like!

Video start: "Lets come up with a really big number." Video end: "The destruction of the universe by blackhole dominance."

@MisterHunterWolf

4 жыл бұрын

Sounds like a vsauce video to me.

@jpmar1908

2 жыл бұрын

Didnt get it at the start of the video and now i'm wheezing

@dAvrilthebear

2 жыл бұрын

News headline: "Scientist Invents a Number that Destroys the Universe"

@oatmilk9545

17 күн бұрын

sort of interrelated

Rayo: "I'm about to end this man's whole abacus"

@atchaaa

2 жыл бұрын

@xXNumberblocks 100 The Cooler And The CreatorXx abasus

This says something so incredible about human imagination I’m not sure how to put it into words.

@Theraot

3 жыл бұрын

That's precisely it. We are limited to what we can put down into symbols.

@matthewhubka6350

2 жыл бұрын

And yet the final answer was “I can’t come up with a bigger number, so let me define a number to be the bigger than anything this dude could put down on the board”

@legendgames128

2 жыл бұрын

Matthew Hubka *expressed in second order set theory*

@blizzard1198

10 ай бұрын

I'VE GOT THE POWER

@blizzard1198

10 ай бұрын

​@@Theraot we aren't.

"So how fast can you write one symbol?" "I don't know, depends on the symbol. I'd say maybe a seco--" "About one Planck time" "O-Oh! A bit faster than me apparently"

@patricktho6546

4 жыл бұрын

But is there a difference in the Sympols if we write so fast, that we cant say, what happens while we write a symbol?

@patricktho6546

4 жыл бұрын

@pyropulse Our understanding of spacetime breaks, when/if we try to watch what happens while we are writing a symbol. That ist very interristing, but how could we know, that these symbols differ?

@angelmendez-rivera351

4 жыл бұрын

Patrick Tho We don't have to know how the symbols are different. The premise of calculation is an abstract concept of writing, we are not required to actually read what is being written.

@caseydeboth2026

3 жыл бұрын

SWAM Ferox a light year is not a measurement of time but rather the measurement of how far light can travel in one year.

@kerbodynamicx472

3 жыл бұрын

I think your limited to the speed of light lol

Sonic the Hedgehog: I'd better not run too fast or I'll create a sonic boom. Tony the Planckwriter: I'd better not write too fast or all of physics will collapse.

@emadgergis6710

4 жыл бұрын

So I ruined the 0 reply thing.

@TimoIvvie

4 жыл бұрын

Too late shows out. *knuckles approves*

@barsozuguler4744

4 жыл бұрын

Underrated comment xdddd

@DrKaii

3 жыл бұрын

Best comment in a while

@hexamethylenediamine7934

3 жыл бұрын

Sonic can run at the speed of light

No matter how big the RAYO's number is, it's still nearer to zero than it is to absolute infinity.

@MakerManX

3 жыл бұрын

Well you aren't wrong but it applies to every number anyway

@euphoriaggaminghd

2 жыл бұрын

Yes but thats because infinity describes a concept. As a number there is no integer close to it because infinity-1 is not real. You can't count to a finite amount and say its close to infinity.

@sergecjprojects8429

2 жыл бұрын

Absolute infinity is a bit bigger than you think

@murchmurch7678

2 жыл бұрын

The part that says: you would know it. That cant happen. Its impossible. We cant use it. There isnt enough bits of data storage in the universe to that so its not possivle to define it , so its not a valid number. Am i right?

@sergecjprojects8429

2 жыл бұрын

@@murchmurch7678 no, the reason absolute infinity is much much bigger is because it is much much bigger than regular infinity, let alone Rayo's number

I think the fact that these numbers come to an end fascinates me more than infinity

I really love the idea of the guy just drawing a line through all the 1's to make a string of factorials. That's so clever and elegant.

@pinkman_

3 жыл бұрын

I honestly love that more than Rayos number

@pedrofellipe8028

3 жыл бұрын

He's the winner in my books

@doicaretho6851

Жыл бұрын

Yeah but he lost in the end.

@O-Kyklop

Жыл бұрын

He would have lost anyway, simply because 11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! equals 0.

@user-dh8oi2mk4f

10 ай бұрын

@@O-Kyklop how?

Tony: I'm not really sure we can get bigger than this. Future Tony: So uh, ....

@djinn666

4 жыл бұрын

Let M(1) be the largest finite number that can be defined by 1 mathematician working for 1 year. I define M(n) is the largest finite number that can be defined by M(n-1) mathematicians working in perfect harmony for M(n-1) years.

@guyingrey1072

4 жыл бұрын

​@@djinn666 M(Tree(10^100))!!!!!!!!! (Those are factorials)

@birthsonbluebell3654

4 жыл бұрын

@@guyingrey1072 Factoriala have already been used. Googol has already been used.

@arthurthekyogre9155

3 жыл бұрын

@@djinn666 there is no largest finite number

@spipsdew6157

3 жыл бұрын

@@arthurthekyogre9155 but there is a largest finite number that can be defined by 1 mathematician working for 1 year.

This video was just great. Big moves from Elga in the first few minutes with that spectacular flourish. Ends with contemplating the destruction of space-time. 10/10

4:31 That little "Turing Inside" made my day 🤣

Day 20 of quarantine: Calling numbers daddy now

@variousthings6470

4 жыл бұрын

@@Nogli "This guy"

@rickharper4533

3 жыл бұрын

@variousthings “absolute unit”

@OrpheusWasAPoorBoy

3 жыл бұрын

Flashback to when the quarantine was only 20 days long

It's so awesome that you talked about this. I watched this in person when it happened! The room was indeed packed, but it wasn't a very big room. :)

@adamdorsky5465

2 жыл бұрын

Did the guy actually do the factorial thing?

@CoolerQ

2 жыл бұрын

@@adamdorsky5465 IIRC factorial was used as one step ("you can add a bunch of factorials here"), but then the rules didn't allow reusing the same mechanic again.

@adamdorsky5465

2 жыл бұрын

@@CoolerQ That’s still cool though

@suhail_69

2 жыл бұрын

Is there any video recording of this?

@JoshuaWillis89

2 жыл бұрын

That’s amazing

2:06 From what I read (the MIT newspaper _The Tech_ did a report on the event), Elga actually went first by just writing the number 1, then Rayo added a bunch more behind.

I would have loved to attend this historical event ! I can imagine the whole room going crazy after that second move...

The googol seems pathetically tiny now, since Graham, Tree, BB and Rayo.

@angelmendez-rivera351

4 жыл бұрын

This statement is false: The funny thing is that there are plenty of valid googolisms larger than Rayo's number. It's true that some of them are debatable and possibly ill-defined, but some, such as Fish(7), BIG FOOT and Little Biggeddon are so huge that Rayo's number is tiny in comparison, and they rise from different mathematical theories and constructions than Rayo's number, and these theories have been formalized, and mathematicians have agreed on the well-definedness of these numbers.

@DuhLeeSinguh

4 жыл бұрын

@@angelmendez-rivera351 so are you saying that this entire video was a lie? Because at the end you can see that they stated all the numbers you named do not best rayos number.

@condoti

4 жыл бұрын

You have a cool name.

@superlightningsam4503

4 жыл бұрын

DuhLeeSinguh They would, but some of them are ill-defined and don’t count until the issues with them are fixed.

@nanobak

4 жыл бұрын

It still covers an important role by being the smallest stupidly large number

Three. Take it or leave it.

@lynk_1240

3 жыл бұрын

How about I TREE it?

@terminat1

3 жыл бұрын

3 isn't a terrible choice. It's larger than infinitely many real numbers, after all.

@number_8903

3 жыл бұрын

I think π

@AlexLuthore

3 жыл бұрын

Tree!

@RocketboiC4

3 жыл бұрын

Well it’s bigger a infinity of intergers(I’m not lying it’s true) -infinity

I love the passion this guy has for mathematics.

I love super high intelligent stories that can somewhat simplify for us peasants to understand a fraction of it. Beautiful.

More than the number itself, it shocks me how he managed to pull off that monster definition on the fly, using nothing but chalk and a blackboard. Some people are just crazy.

"Have we got enough time to write that down?" Ok, maybe, it can't be that big, 10^48 is a lot but come on- "Well that kinda depends on the nature of dark energy" *OH*

@tomc.5704

4 жыл бұрын

We would also run out of matter to write with. As we're crafting our "Biggest number based on first order set theory", we have about 10^20 more symbols to work with than we have particles in the universe. You can define particles as molecules, atoms, or quarks--it doesn't make a difference. There's only ~10^80 of them, give or take a few zeros. And THEN we have to actually evaluate that string of symbols. They evaluate to an integer---the biggest possible integer we could build with 10^100 symbols. If you can define a big function, but you used fewer than a googol symbols---your function was too small. If you used all googol symbols, but your function wasn't perfectly optimized to be as big as possible--your function was too small. RAYO(10^100) is one bigger than that.

@angelmendez-rivera351

4 жыл бұрын

Tom C. Not necessarily. Just assume that all symbols are being written on top of one another. It's not necessary for the sentence to be humanly legible, it just has to be written.

@Nosirrbro

4 жыл бұрын

@@angelmendez-rivera351 By that metric just writing RAYO(10^100) counts as writing it. Its not humanly legible, but all of the information is there.

I love how there's numbers that are so big we can't physically write them down we can only prove their existence via abstractions of a previous "big number idea" that's why I love math it's like the coolest video game you could ever hope to play where the player is in control of the whole universe restricted only by the collective level of creative thought of the playerbase.

“But we can write it down” *smiles

THAT REALLY SHOCKED ME WHEN ELGA DID THAT 11!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

@drex5242

4 жыл бұрын

HunterWolf X r/unexpectedfactorial

@ProDyel

4 жыл бұрын

He takes the spiritual win for sure.

@fahadb3142

4 жыл бұрын

HunterWolf X wow you are that shocked

@madlad255

4 жыл бұрын

He was probably inspired by people who type like this: :) 'OMG SO COOL 1!!!1!1!1!1!1!!!!1!1!1!1!1!1!1!!!1!1!!1'

@barsozuguler4744

4 жыл бұрын

Not even brutal because this number breaks universe xdd

padilla and big numbers. name a more iconic duo

@YellowToad

3 жыл бұрын

me and youtube

It's amazing to me that we as part of the great ape lineage can conceptualize numbers so enormous. I do love how it stimulates my brain thinking of these things as we all do I suppose.

@magnusnilsson6217

3 жыл бұрын

Yes. That's a great perspective

@meehaerospace1476

2 жыл бұрын

you make sense but when you say it like that you also sound like an alien trying to hide among humans

u can tell prof. padilla loves his job.He is so passionate and enthusiastic.

What's clever about Rayo's number is that it uses our own way to describe mathematics as the weapon that makes it such a large number.

"Rayo's Number plus one !!", screams my inner child voice.

@anadaere6861

3 жыл бұрын

I wonder what would happen if you put Rayo's Number/the smallest possible value

@charizella

3 жыл бұрын

@@anadaere6861 there is no smallest possible value

@anadaere6861

3 жыл бұрын

@@charizella i think they call it infinitesimal

@KingdaToro

3 жыл бұрын

@@anadaere6861 ERROR: DIVIDE BY ZERO

@alexeyvlasenko6622

3 жыл бұрын

@@charizella Sure. But, to put it more precisely, what is the smallest positive integer larger than any positive integer that can be expressed in 10^100 symbols in set theory, multiplied by the largest nonzero positive real number smaller than any nonzero positive real number that can be expressed in 10^100 symbols in set theory? Is it possible to at least prove that this number is greater than 1, equal to 1, or less than 1?

I always believe this episode is the last and the best one of the big number videos. The big number dual is just fantastic. Now more than ten years past though, most modern big numbers still use set theory to express big numbers.

It's interesting to think about how to play the game of coming up with large numbers: is it to come up with the biggest number you can think of, or to come up with the smallest number you can think of that is bigger than the previous one? The latter would allow you more future moves and more thinking time, but the former ensures that, if your opponent's biggest number is the same as yours, you get to play that move.

Assuming I'm understanding correctly, it's extremely interesting to note that writing RAYO(10^100) in the first-order set theory language it's designed from would be by far the most efficient way to express that number accurately. The best way to express Graham's number is using arrow notation. Takes a minute or two for a human to write the full formula, tops. The best way to express RAYO(10^100) is the exact method that would take a computer 10^56 seconds to write at a pace far faster than what is physically possible.

@kesleta7697

2 жыл бұрын

Wouldn't the way shown in the video at 11:32 (using second order set theroy) be far more efficient?

@steffenbendel6031

8 ай бұрын

But since he defined that number with far fewer symbols than 10^100, wouldn't that be a contradiction?

@crazybeatrice4555

7 ай бұрын

He used second order not first order

@steffenbendel6031

7 ай бұрын

@@crazybeatrice4555 no I understand why the first order was so weak. Second Order rules.

@XnoobSpeakable

6 ай бұрын

Wouldn't the best way be "RAYO(10^100), where RAYO(n) is defined as [insert definition]"

I think every time Prof. Padilla comes with a bigger number than before, we should always remember in the comment section that is basically 0 compared to infinity.

@RobertCroome

4 жыл бұрын

Is it though? Can infinity really be considered more than the largest number you can make be moving all the molecules in the universe to represent a number?

@ThiagoGlady

4 жыл бұрын

@@RobertCroome Yes. We can make a bigger number if we use our minds. Always.

@gaeb-hd4lf

4 жыл бұрын

@@ThiagoGlady Infinity is a concept not a number, so technically you can´t compare them...

@ThiagoGlady

4 жыл бұрын

@@gaeb-hd4lf Yes I can. You are not in a room with mathematicians. Casually, you can compare anything you like.

@heyandy889

4 жыл бұрын

actually 3 blue 1 brown has a video about this today!! it's about "zero" probability events, like picking a particular irrational number. if you pick a number between 0 and 1 you must end up with some number ... but all numbers in the interval have probability 0 of being picked. yeah my brain puckers when I think about that, like I'm chewing on a sour patch kids.

This is my absolute favourite numberphile, with "All the numbers" in a very close second place

I understood nothing, yet I enjoyed the video because of this man's enthusiasm.

My brain is still hurting from Graham's number! (Although it started hurting from 3↑↑↑3 onwards. The forth arrow did not even fit into my head) And now this? WOW!

@KalOrtPor

4 жыл бұрын

It helps to consider 3↑↑↑3 as 3↑↑(3↑↑3), which is 3↑↑(7,625,597,484,987), and then picture writing out 7.6 trillion 3's from here to the sun! Since 3^3^3^3^3 is already bigger than googolplex, you can imagine what working out the trillions of layers does! Then 3↑↑↑↑3 = 3↑↑↑(3↑↑↑3), but that's the same as 3↑↑↑(3↑↑7,625,597,484,987), which means you write out 3↑↑3↑↑3↑↑3↑↑.....↑↑3 for 3↑↑7,625,597,484,987 times. So three arrows gets the unimaginably huge number 3↑↑(3↑↑3), but with four arrows, that unimaginably huge number becomes the number of 3's in another sequence of 3↑↑, and multiplying that all out becomes the number of 3's in another 3↑↑, and so on for that unimaginably huge number of times. Of course, instead of going to 5 arrows, going to 3↑↑↑↑3 number of arrows in G2 is mindboggling. But taking G(G(G(....G(64) a Graham's number of times is still nothing to TREE(3), which is nothing compared to this. I like Graham's best though because it can be related how to get to it. TREE(3) you can't really get any sense of scale or stepping up to build it, but at least it also describes something tangible and it has an exact value we could run a program to calculate (if we had enough time and resources!). Rayo's is an interesting concept, but it's not computable and has little meaning outside of saying "this defines a really big number however big you're able to define it".

@flickflack

4 жыл бұрын

At least Graham's Number has a point, abstract as it is. This is just a big number with some arbitrary rules tacked on.

@CaptainSpock1701

4 жыл бұрын

@@KalOrtPor That is a very detailed reply! Thanks, it is much appreciated. I do understand the 3^3^3... in my head. It makes sense. But a tower of 3^3^3... 7 625 597 484 987 times breaks my brain. But I do agree with ​flickflack. At least it has a point.

@XtreeM_FaiL

4 жыл бұрын

KalOrtPor You're not helping at all. :|

@coolguy284_2

4 жыл бұрын

@@KalOrtPor Nice reply, but can you close your parenthesis after all the Gs?

Idk why but when he said "but we could write it down" it just seems so comforting, w with everything happening right now it's oddly nice to think that we could be around in 10^48 years still creating things and being curious. In that many years everything that we're going through right now won't matter.

7:00 The answer is definitely yes. Tree(10^100) is computable.

@Owen_loves_Butters

Жыл бұрын

BB grows faster than TREE, but that only means that BB(n)>TREE(n) at some point, where that point is is probably not knowable.

@XnoobSpeakable

6 ай бұрын

​@@Owen_loves_ButtersI decuded to dig deeper into this while talking in a discord server once I sadly forgot most of the details of how these functions compare exactly But I bet that the n is quite small, I'd bet around 10^10 or so, if not less

@XnoobSpeakable

6 ай бұрын

I just came up with this estimate on the spot If I remembered the details from my previous deeper dive, I could give a better estimate

honestly, while its impressive how big this number is, I find Tree(3) more compelling due to the combination of being so straightforward and powerful.

5:42 I think your beaver accidentally used telekinesis.

@connerfinch2744

3 жыл бұрын

Hahah i saw that

@Theraot

3 жыл бұрын

Yep. Here is your problem. Someone set this thing to telekinesis.

@shambhav9534

3 жыл бұрын

No, I think the animator used telekinesis.

@agimasoschandir

3 жыл бұрын

quantum tunneling

@shambhav9534

3 жыл бұрын

@@agimasoschandir Beavers' wavelength is too low for that to happen.

Tony loves endangering the fabric of our universe to make his big numbers huh

@oz_jones

3 жыл бұрын

"Haha big numbers go brrrr" - Tony

Tv screen when you get a strike: 7:44

Thanks for these videos Numberphile. Appreciate it so much.

And still just as far from infinity as 0.

@martinh2783

4 жыл бұрын

Yea, it really is a quite small number.

@mohammadfahrurrozy8082

4 жыл бұрын

Math are awesome!

@priyansh1210

4 жыл бұрын

actually closer to 0 than to infinity

@Pieter31

4 жыл бұрын

@@priyansh1210 The wording can be interpreted in 2 ways, but I assume he meant that 0 and rayo's number are both an equal distance apart from infinity.

@esquilax5563

4 жыл бұрын

I find that extremely large finite numbers give a much richer sense of infinity than infinity itself

“Numberphile, I need your strongest numbers!” “My numbers are to strong for you traveler, you’ll have to find someone who philes WEAKER numbers!”

@pgame20

3 жыл бұрын

My quooooootients are much too strong, travelerrrrr!

@waharadome

3 жыл бұрын

Number seller!!

@qwqwqwqw99

2 жыл бұрын

But I'm going into battle!

@Zephyrus601

2 жыл бұрын

I don’t have time for your games

"Busy beavers in a dark room!" - add it to my grindr profile.

@grantwilliams2650

3 жыл бұрын

...oh

@rayelgatubelo

28 күн бұрын

Uh, but beaver is kind of the euphemism for the female organ. Unless you're talking transmacs. But most transmascs I know dislike the discrimination they're subjected to in Grindr.

I'll be honest: When he got to the super busy beaver section, I was more or less completely lost. I still enjoyed the entire video, the concept, and the scale described at the end. Hats off to those two professors, the hosts, and any audience member who could follow it all! I'm requesting a much higher IQ in my next iteration.

"Ugh... Who put the beaver in energy saving mode again ?"

@agimasoschandir

3 жыл бұрын

It's Energy Star compliant

When you bring the idea of " I'm thinking your number +1" to a way new level

@jobigoud

4 жыл бұрын

I don't get why this part is needed. Just saying that it's the biggest number that a mathematical language of 10¹⁰⁰ symbols can express seemed enough to me, knowing the other contestant can't use the +1 trick.

@patricktho6546

4 жыл бұрын

@@jobigoud To do the +1 "trick" you need more symbols, so it can't work even without forbitting it in the first place.

I love these big number videos. 10:08 How do those sets of symbols work out to zero and to one? We need a video on set theory that explains this! That looks absolutely fascinating.

@felixmerz6229

Жыл бұрын

There exists "∃" a set x1 "x1" where there doesn't exist "¬∃" a set x2 "x2" where x2 "(x2" would be an element of "∈" x1 "x1)". This is a little awkward to read, but I tried to avoid grouping symbols to make sure their individual meaning becomes clear.

Why is it defined in terms of first order set theory? Would it be equally valid for him to have said "the smallest number that can be expressed in the English language in a googol words"?

@entropie-3622

11 ай бұрын

That would not be properly defined which can easily be seen by then stating "the smallest number that can be expressed in the English language in a googol words plus 1" which is clearly bigger than your number but expressed in less than googol words so it is also smaller than your number. Which is why we can not use English language as the foundation of logic.

Never clicked on a video so fast in my life, I would never get tired of this subject :D

@aok76_

4 жыл бұрын

I've always seen this comment on videos. Today I know why people comment it.

@maazahmed2341

3 жыл бұрын

@@aok76_ Its for da likes man

Every time I watch a video like this I’m reminded of my own mortality and I get real sad

@agimasoschandir

3 жыл бұрын

Time for a Daisy break

I probably should not have carried on watching Numberphile videos this late. My brain now hurts :O

Yeah, bringing up ones to a factorial fight. This is like bringing up a knife to an intergalactic war between level 3.5 civilizations.

14:34 Reminds me of the game "Universal Paperclips." The time in which we've converted all matter in the universe to chalkboards and chalk and life support in order to keep writing the number =P

@raptorcharly8055

4 жыл бұрын

As a fan of that game, damn you're right

Those math dudes always smiling all the time its so sweet how much they are in love with math

Don't know what the real situation was during the duel, but the way Tony described it makes me feel that by the time Rayo put out the Busy Beavers, Elga lost already. It's like Rayo just set a trap for Elga to fall and unfortunately Elga fell in (or else he could have gone anything other than super turing machine). It would be very funny if Rayo shouted the Busy Beavers out just to buy him time to think of the way to define a number so that Elga can no longer rescue himself from the trap.

I wouldn't know how to state this non-semantically, but imagine a tree like construction, that is constrained by an orthogonal grid, and a new seed at 90 degrees is treated as being different to a seed at 180 degrees. three colors of seeds and 10^100 dimensions. the angles and directions of the branches is what defines a tree to be unique.

10:12: zero (or empty set) as expressed in symbols of first-order set theory. 10:26: one (or singleton) as expressed in symbols of first-order set theory.

@jonipaliares5475

4 жыл бұрын

So the symbols that appeared on 10:26 represent two, right? I'm quite confused because they did show up when he said "one"

@viliml2763

4 жыл бұрын

​@@jonipaliares5475 Yes, you're right, it's confusing.

@Jop_pop

4 жыл бұрын

@@viliml2763 EDIT: what I originally wrote below is wrong. The commenters who say the 10:26 logic represents 2 are correct. Actually 0 = {} 1 = 0 U {{}} ={{}} 2 = 1 U {1} = { {}, {{}} } And if you decompose the logical symbols at 10:26 you get 2, not 1. Original post: actually the one that appears at 10:26 does represent 1. In set notation it's { {}, {{}} }. That is the set which contains the empty set and the set containing the empty set. This represents 1 according to the von Neumann construction, where 0={} (empty set) and the successor(a) = a U {a}.

@jonipaliares5475

4 жыл бұрын

@@Jop_pop I don't think I understand, why isn't 1 represented as {{ }}? shouldn't it be just the set containing the empty set?

@Jop_pop

4 жыл бұрын

@@jonipaliares5475 see the edit I made to my comment. You're totally right, my mistake!

I love how he went from largest numbers to astrophysics and plank time and Dark Energy... 😂 wow

@chandrabitpal9151

4 жыл бұрын

Dude this is natural nothing is special about this when u do number theory related maths u r ought to know at least this much physics

@User-ei2kw

4 жыл бұрын

@@chandrabitpal9151 chutiya

@morgiewthelord8648

4 жыл бұрын

User 1 aeh?

@shikharsrivastava5020

4 жыл бұрын

@@morgiewthelord8648 it's the term for asshole in hindi

@technoultimategaming2999

4 жыл бұрын

Hey Vsauce Michael here! But what is the largest number?.... .... and that's how we will die in 10^34 years

SSCG (3) ^ SSCG (3) ^ Googolplex ^ Rayo's number ^ TREE (3) ^ 97 Duodecillion ^ SSCG (3)

5:43 was it really intended that the light to the left of the robot turns off?

I've watched these since the beginning. This prof is the only one that hasn't aged a day!

And when the entire number is written, the first second of eternity will have passed

@sophiegrey9576

4 жыл бұрын

Not even, no. The first instant of eternity.

@eldaneuron4183

4 жыл бұрын

Bird sharpen his beak on the mountain

The factorial idea was really cool!

I'm wondering, if you did something like arctan(pi/2 - 1/[the number the other guy wrote]), how would they be able to tell if future numbers were bigger or smaller.

@Math_Drag0n

Жыл бұрын

they dont

@gabrielesalvatori6804

Жыл бұрын

pi is not finite thought

@yyattt

Жыл бұрын

@@gabrielesalvatori6804 Pretty sure it is. It's possible to write a finite number that's larger than pi. 4, for example.

@skya6863

10 ай бұрын

​@@yyattt check it with a graphing calculator, tan(pi/2 - 1/x) approaches x as x goes to infinity, in fact it is a slightly smaller number

@yyattt

10 ай бұрын

@@skya6863 Haha! Turns out I'm not as smart as I thought! Well done for spotting the fatal flaw in my plan.

This channel is a hero for uploading a video on this number

*sees title of video, smiles* "Ah, another classic big number Numberphile video" *clicks video*

This is wild! Thanks for the upload ❤

6:30 I wonder if theirs a limited number of stages without number manipulation. For example. Stage 548: If the BB notices theirs x amount of lights on in a row, BB will switch x amount of lights.

BB(10^100) >>>>>>>>>>>>>> ... *unimaginably many greater thans* ... >>>>>>>>>>>>>>>> TREE(10^100) > G(10^100) For anyone wondering.

@pizzapabpro3160

3 жыл бұрын

Proof?

@gpt-jcommentbot4759

3 жыл бұрын

@@pizzapabpro3160 yes, it is known to start slow and grow asymptotically faster than any function that could ever be computed within the fast growing hierarchy in any effective way, these computable numbers include the G's, TREES, Bucholz hydras, loaders number, the simple or normal subcubic graph numbers, goodsteins function. Unconputable functions include rayos function, the FOOT function, DOODLE function, xi function, and BB function. They each have comparable but can grow faster than others. Here are the BB function: BB(1) = 1 BB(2) = 4 BB(3) = 6 BB(4) = 13 BB(5) > 4098? BB(6) > 10^18267 BB(7) > 10^10^10^10^18,705,352 It is clear than BB(6) >> 27, lets use this extremely lower bound to compare higher numbers BB(8) >> 7,600,000,000, (for a closer bound, this number is most likely within the range of tritri, but its my guess) BB(10) >> TriTri = 3^^^3 (knuths arrow notation) BB(12) >> G1 = 3^^^^3 Lets use the fast growing hierarchy, for quick demonstration f3(3) > 120 million digits, yeah, I hope you have a median understanding of the fast growing hierarchy. BB(38) > fω2(167) >> Grahams Number BB(85) > fε0(1907), to give a clue what this means, fε0(n) = fω^...for n times...^ω, fω^ω(n) = fω^n(n), fω^2(n) = fωn(n), fω2(n) = fω+n,grahams number is between fω+1(63) and fω+1(64), and believe me grahams number is outright HUGE. BB(38, 3) >> fε0(200,000,000), It only grows faster, were nowhere close to a googol in fact we havent reached then 3rd digit yet and were smashing numbers, I am not sure if these numbers are more than TREE(3) yet (no it is not due to TREE(3) being way more than gamma 0), however over time the sequence will outgrow it. This is horrifically simplified, in fact you have to be a intermediate googologist to proffesionally describe it (which im not)

@laxxius

3 жыл бұрын

@@pizzapabpro3160 well beyond what I can understand

@laxxius

3 жыл бұрын

@@user-kz6zm3ij5f small

@gpt-jcommentbot4759

3 жыл бұрын

@@user-kz6zm3ij5f unconparable. TREES are much faster than Gs, BB(10^100) >>>>>>>>>>>>>>>>>>>>>>>>>>>>...Unimaginably greater than later...>>>>>>TREE(TREE(10^100)) >>> G(TREE(10^100))

Imagine living for Rayo(bb(Tree(10^100))) years. Might as well be infinite. When some people wish they could live forever they don't actually understand how mindbogglingly incomprehensible it would be. You would just wish for death, or maybe you've gone so insane you wouldn't undestand the concept of death or concepts in general.

@lenudan

4 жыл бұрын

The total energy required to power a human brain to comprehend that near infinite reality...even if you only had 1 brief thought about it every 10^100 years, would still be greater than the total combined energy output from every star in every galaxy in every universe throughout a Graham's number of Universes...

@jimi02468

4 жыл бұрын

I like that number. It's like a function sandwich. Here's a better one: Rayo(BB(Tree(G(10^100))))

@ssayani87

4 жыл бұрын

@@jimi02468 I think I shall have to 1-up with: Rayo(BB(Tree(G(10^100)))) + 1

@Yous0147

4 жыл бұрын

Absolutely. Here's something even more bonkers. Essentially 0 or Rayo(bb(Tree(10^100))) are practically speaking both equally far away from reaching infinity.

@jordanrodrigues1279

4 жыл бұрын

Put down the Universal Perspective Vortex before someone gets hurt.

When writing 1 symbol per plank time the total distance the tip of the pen travels on the paper needs to be equal to 1 plank length or it will be impossible to write the symbols that quickly

I’d throw my hat in the ring with the first googalplexian factorial (1 followed by a googalplex (1 followed by a googal zeros) zeros) prime numbers strung up like graham’s number (2^3^5^7^…)… But I think you could define that number in first order set theory in way less than 10,000 characters being generous That is one way to describe how large rayo’s number truly is

This is wonderful. I love the animations, especially Rayo writing down symbols.

"You wrote the wrong symbol on that board." "Why didn't you tell me earlier? I've already gone through 50 other boards!"

If you are writing one symbol per planck time, what time does it take to drag your chalk a certain length across the board to write the symbol?

alepnol, omega, and epsilon: allow us to introduce ourselves.