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00:00 - 11:0012:00 - 00:00

00:06
@LeakyNun yup
@SimplyBeautifulArt where are all the people on discord
@LeakyNun It's a game where we take turns writing numbers
you in particular
I was doing some stuff
also, could you trash this?
@SimplyBeautifulArt let's go
no using SOAP :P
00:07
:P
So, I start with the almighty 0
could you trash that first?
I continue with the obligatory 1
thanks
2nd triangular number
00:09
Hey @Nilknarf
Join this game
And the antimatter dimensions
hey, ok
0_0
Wait, is it my turn?
googol
00:10
Just don't go twice in a row
wow we're getting big now
You guys are off to a slow start XD
googol[googol]googol
00:10
?
hyperoperation
what is that supposed to be? googol^3?
OH
NO
hydroxyl radical
u said we were too slow
00:11
nitrogen monoxide
Hm
Ack(googol+10,googol)
Ack(googol+10,googol)+1
someone has to do it
heh
Can't do that
The rules are that once someone claims a function
00:13
Just be sportsmanship
like "Ack"
then nobody else can use it
oh, really
Nilk, your turn
hold on, I'm going to define something.
00:13
lol
someone else can go while I'm working this out
Dang it
Ack(Ack(5,5),5)
Ok, I've got a function ready
Shoot
I didn't get to use my newest function
00:15
$$\Phi(x)=x\uparrow ^x x$$
$$\Phi(x_1,...,x_n)=\Phi(x_1,...,x_{n-2},\Phi(x_1,...,x_{n-1}), x_n-1)$$
Heh heh heh heh heh
Uh... so you simply discard the last element?
Makes it kinda useless to do nestings...
Oh whoops
No, I don't
Sorry, I left that out
Gosh darn it, now we have to analyze this function.
00:17
Okay, I'm going now
$\Phi(\text{googol},\text{googol})$
...I think that is bigger
8
Q: Growth rate of the nth natural number not constructable with n steps of addition and multiplication

Simply Beautiful ArtWhile messing around with the idea of ordinal collapsing functions, I stumbled upon an interesting simple function: $$C(0)=\{0,1\}\\C(n+1)=C(n)\cup\{\gamma+\delta:\gamma,\delta\in C(n)\}\\\psi(n)=\min\{k\notin C(n),k>0\}$$ The explanation is simple. We start with $\{0,1\}$ and repeatedly add it...

what is sportsmanship? can I go like
I wanted to use this function
But I guess its a little bit late for that
@SimplyBeautifulArt well that function isn't that fast
00:18
Did mine pass that?
BB(googol), I win
No uncomputable functions
Nope, I've tried that before XD
simply got mad at me
XD
00:19
Cuz the game ends really fast that way
alright
seriously, I need to analyze that function :P
What is it?
It's taking longer than a second...
00:20
His number is $\approx f_{\omega+1}\rm(googol)$
well, Phi(G,G) = Phi(Phi(G),G-1) = Phi(Phi(Phi(G)),G-2) = ... = Phi^G(G)
ninja'd
Correct
Well, the point is that if someone makes a new function
You don't go copying it
Is someone else gonna go?
your function is omega+1 in two arguments
you shouldn't have wasted it by providing only two arguments
00:21
:(
I'm bad at ordinals :P
$$f_{(a,b)}(n)=\begin{cases}n+1,&a=b=0\\ f_{(a,b-1)}^n(n), &b>0\\ f_{(a-1,n)}(n), &\rm else\end{cases}$$
holy god
Oo
I assume the superscript is iteration, and not exponentiation
00:24
My number shall be$$f_{(1,2)}\rm(googol)$$
And yes, iteration
Number is $=f_{\omega+2}\rm(googol)$
Oof, I don't even know how big that is
oh god
I'm so uncreative
you guys create functions
@SimplyBeautifulArt even created the fastest function
how do you even create those
It is approximately $$\newcommand{glog}{\rm googol}\Phi(\glog,\glog,\glog)$$
00:25
I'm just going to go with Goodstein(googol)
@LeakyNun Magic and training
@Nilknarf did you just create a new benchmark function
Hm
googol = 10^100
oh, so Phi(G,G,G,...,G) is f_(omega+n-1)(G) where n is the number of arguments
≈ 1000^33
≈ 2^330
00:27
hahaha
go on @SimplyBeautifulArt
≈ 2^2^8
= 2^2^2^(2+1)
Goodstein(googol) ≈ $f_{ω^{ω^{ω+1}}}(3)$
3 tower's of ω
how does that work?
You replace the 2's with ω's
fair enough
00:29
Taking the leading ω^x power
It is approximately f_x(3)
I gotta go eat
@Nilknarf your turn :P
Go get addicted to antimatter dimensions
Ugh, I think $\Phi$ is dead
It won't load! D:<
Okay, I gotta go now
00:34
@Nilknarf :'(
@Zacharý welcome!
What is the purpose of this room? Just to converse about stuff for calculation?
@Zacharý well I mostly come here to learn about ordinals
Or would you say you ordinal-ily come here to learn about ordinals?
stares
@Riker hi
@LeakyNun (& @Riker) And you have a lot to learn, Commander Leaky Nun.
00:43
@Zacharý sure
(I have no clue, I had to do a star trek quote)
I'm back @LeakyNun
@SimplyBeautifulArt welcome back
your turn
@yaa09d hi
00:56
I don't have any spectacular notations I can make off the top of my head that surpass ε_0
Oh wait, I do
Oh wait, nvm
Have you been playing antimatter dimensions? @LeakyNun
@SimplyBeautifulArt shamefully, yes
Hehe
How far did you get?
I just reset the game for the second time
so I'm aiming for 6D
LOL
I have no life
you?
> How much antiwood could an antiwoodchuck chuck if an antiwoodchuck could chuck antiwood?
00:58
I've already done 1 antimatter galaxy + 8 resets
> The fatter catter satter on the antimatter.
@SimplyBeautifulArt indeed no life you have
@SimplyBeautifulArt where did you learn all this ordinal sith rabbit hole
idk
Mostly on Discord I think
Well I'm out ...
01:00
Cya @Zacharý
@SimplyBeautifulArt from whom?
Some assistance from others
what what?
that's amazing
01:01
:P
Should I do a dimension sacrifice?
is there an uncomputable countable ordinal?
I'm doing it
or non-recursive countable ordinal?
gamma?
01:02
No, any computable ordinal is countable
that isn't incompatible with what I said
Gamma ($φ(1,0,x)$) is computable
@LeakyNun But the Church-Kleene ordinal, for example
In fact, any ordinal between the Church-Kleene and $\omega_1$
hmm
you're constantly blowing my mind, you know
i study maths in imperial
and you still blow my mind
imperial?
:P Well, blowing minds is what I try to do
@SimplyBeautifulArt imperial college london
01:06
Btw
There's this achievement on antimatter dimensions to reach infinity (a.k.a. 10^308) using only the first dimension and timespeed
but why
I'm scared
x'D
90 byes of the 8th dimension!
Woot woot!
@LeakyNun and that's cool
@SimplyBeautifulArt I mean, groups, topology, cohomology, algebra, they're all cool
but nothing compares to ordinals
it's the most beautiful thing I've ever encountered
seriously
01:09
say
How do you feel about ordinal collapsing functions?
what is your statistics?
You have made a total of 39.88 Qt antimatter.
You have done 2 soft resets.
You have 0 Antimatter Galaxies.
You have played for 7 hours, 53 minutes and 50 seconds.
If every antimatter were 65.84 M zeptometers cubed, you would have enough to make a proton.
@SimplyBeautifulArt I haven't read much about them yet
lol
You have made a total of 50.48 OQa antimatter.
You have done 9 soft resets.
You have 1 Antimatter Galaxies.
You have played for 19 hours, 44 minutes and 52 seconds.
If every antimatter were a planck volume, you would have enough to make 16.02 M hypergiant stars.
^ 16 M hypergiant stars
... what the heck ... are these actual terms?
x'D
@Zacharý ivark.github.io
Get addicted
@SimplyBeautifulArt I'm just making protons
you're making stars
01:15
So ... it's cookie clicker without clicking on a cookie.
@Zacharý enough with the puns stares
@LeakyNun That is not a pun, it's a comparison to a popular (or at least it WAS) popular, phenomenon.
> What do you mean, more than two dimensions??? We're on a screen, clearly there are only 2 dimensions.
@Zacharý what do you mean?
Look up Cookie Clicker.
I see
> If you open an anti-lootbox, are you selling random possessions for in-game currency?
> If an alien lands on your front lawn and extends an appendage as a gesture of greeting, before you get friendly, toss it an eightball. If the appendage explodes, then the alien was probably made of antimatter. If not, then you can proceed to take it to your leader. -Neil deGrasse Tyson
01:27
Wouldn't it explode on contact with the air?!
> A new chat server has been created for Antimatter people to spy on Matter people, and the world has fallen into chaos and discord
*and it was on Discord, of course
> But to an antimatter person, wouldn't they be matter and we antimatter?
WTF is this from?
@Zacharý Join the game
01:33
I am on it now
> If every antimatter were a planck volume, you would have enough to make 3.25 K Oort clouds.
wtf?
I'm half-way to infinity
Probably means I broke past 10^150 antimatter
> Antimatter is honest, matter makes up everything
@SimplyBeautifulArt I reset the third time: now waiting for 7D
How long have you guys been playing for??
> You have played for 20 hours, 11 minutes and 40 seconds.
01:38
Where does it say this?????
I reset
Under statistics
3 minutes later...
@LeakyNun So much boost lol
@SimplyBeautifulArt I'm creating a function that is heavily inspired by binary-Veblen
one might ask what the point is, to which I reply "I have no idea"
same
I reset and I've already got some walls of chinas
01:45
Question: does this use e^t for its algorithm or something?
Now making asteroids
@Zacharý probably
#dank-maymays
Pattern-matching notation (discard-upon-first-match)
$\delta(0,0,0) = 0$
$\delta(0,y,0) = \sup\{\delta(0,b,0)+1 \mid b < y\}$
$\delta(x,y,0) = \sup\{\delta(a,y,\omega) \mid a < x\}$
$\delta(x,y,z) = \sup\{\delta(x,\delta(x,y,c),0) \mid c < z\}$
a more rigorous/elegant approach to Veblen function
explore :P @SimplyBeautifulArt
01:46
Wait what do you want me to do?
wait, there might be some error
let me fix it first
I'm making dwarf planets
Pattern-matching notation (discard-upon-first-match)
$\delta(0,0,0) = 0$
$\delta(0,y,0) = \sup\{\delta(0,b,0)+1 \mid b < y\}$
$\delta(x,0,0) = \sup\{\delta(a,0,\omega) \mid a < x\}$
$\delta(x,y,0) = \sup\{\delta(a,\delta(a,b,\omega)+1,\omega) \mid a < x, b < y\}$
$\delta(x,y,z) = \sup\{\delta(x,\delta(x,y,c),0) \mid c < z\}$
@SimplyBeautifulArt I want you to explore this function lol
domain is $(\omega+1) \times \operatorname{On} \times (\omega+1)$ for now
01:49
$\delta(0,y,0)=y$
@SimplyBeautifulArt what
$\delta(x,y,z)=z$ nestings of $\delta(x,\dots,0)$ with initial value of $y$.
$\delta(x,y,0)=\omega2$ nestings of $\delta(a,\dots,0)$ with an initial value of $b<y$ and $a<x$.
> If every antimatter were a planck volume, you would have enough to make 298.74 K Suns.
how is sun after star
star is obviously bigger than sun
I reset earlier mate
I'm at red giants right now
$\delta(x,0,0)=\omega$ nestings of $\delta(a,\dots,0)$ with $a<x$ and initial value of $0$.
Hey @Secret
:P Still playing antimatter dimensions?
> If every antimatter were a planck volume, you would have enough to make 1.3 hypergiant stars.
$\delta(1,0,0)=\delta(0,0,\omega) → \delta(0,\delta(0,0,n),0) = \delta(0,0,n) → ... =0$
oh gg
lemme fix
02:02
> None of this matters
@Zacharý How you holding up over there? Lol
> If every antimatter were a planck volume, you would have enough to make 2.2 nebulas.
Enabled cancer notation
You get an achievement for unlocking galaxies with cancer notation enabled
> If every antimatter were a planck volume, you would have enough to make 2.8 Oort clouds.
@AkivaWeinberger Play antimatter dimensions with us
> How does NASA organise a party? They planet.
> If every antimatter were a planck volume, you would have enough to make 3.9 Local Bubbles.
What do you guys think a local bubble is?
oh
> According to no known laws of aviation, there are multiple ways a bee should be able to be swallowed up by antimatter
I haven't seen that one before
02:35
> If every antimatter were a planck volume, you would have enough to make 1.01e3 galaxies.
02:53
Reset!
 
8 hours later…
10:38
$\delta(x,0,0) = 0$
$\delta(0,y,0) = y$
$\delta(x,y,0) = \sup\limits_{a<x\\b<y} \delta(a,\delta(x,b,0)+1,\omega)$
$\delta(x,y,z) = \sup\limits_{c<z} \delta(x,\delta(x,y,c)+1,c)$
@SimplyBeautifulArt $\delta(\omega,2,0)=?$
00:00 - 11:0012:00 - 00:00

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