This is the Realm of Simply Beautiful Art

Simply Beautiful Art

00:54

@S.C.B. Hehe, good luck with your chain arrows. I think I figured out how to beat them

S.C.B.

@SimplyBeautifulArt I don't think I'll be able to participate.

Simply Beautiful Art

Aw

R.I.P. I was just starting to have fun XD

S.C.B.

Daniel Shulkin has been confimed to be secretary of the Department of Veterans.

Simply Beautiful Art

If you were wondering, I'm just now trying fast growing hierarchy

Huh?

And FGH is many functional iterations

S.C.B.

I'm watching the news.

Simply Beautiful Art

01:06

ah

I'm listening, but not watching

By the way, there is basically no chance for your chained arrow to come close to FGH now

S.C.B.

How exactly are your supposed to write how $f(x)$ has a local maximum when $$f'(x)=0, f''(x)<0$$?

Simply Beautiful Art

uh...

Well, if f'(x)=0, it is either an inflection point (f''(x)=0) or a min/max

And due to convexity/concavity, f''(x)<0 implies...?

In terms of FGH...

$$\text{Chain arrows}<<f_{\omega^3}(n)$$

S.C.B.

I meant, should I be elaborating here?

0

Q: What is the local maximum value of the function $f(x) = x^3 + 3x^2 − 24x$?

Give the value of $x$ where the function $$f(x) = x^3 + 3x^2 − 24x$$ has a local maximum. I tried graphing the problem, but I'm still not sure exactly how to find the local max. Could you please help?

calculus

Simply Beautiful Art

Nope, I think that's fine

S.C.B.

OK.

Simply Beautiful Art

01:11

@S.C.B. Have you heard of BEAF yet?

S.C.B.

Exploding Something Something.

Simply Beautiful Art

It's some thing that holds well against FGH

S.C.B.

Growing Quickly.

Simply Beautiful Art

Yeah

But once I reach $f_{\epsilon_0}(n)$, I will exceed BEAF

At least I think I will

Oh, whoops, chained arrows are bigger than I thought

$$\text{Many chained arrows}<<f_{\omega^\omega}(n)$$

And I think my original function is bounded above by $f_{\omega^\omega}(n)$ as well

S.C.B.

OK. I'm not particularly interested though.

Simply Beautiful Art

01:15

Yeah, sorry XD

So how have you been?

S.C.B.

OK. Fine. I guess.

I got a problem wrong yesterday.

The teacher had previously implied all answers would be integers.

Simply Beautiful Art

lol, is it the end of the world for you?

S.C.B.

So when I got a irrational number, I wrote down a different number on the answer sheet.

No, it is a mock test.

Simply Beautiful Art

Oh, wow, ok. That sucks man

Oh, good XD

S.C.B.

All tests I mention are mock tests, not real tests.

At least now.

Tests are only on May, June, etc.

Simply Beautiful Art

01:16

Lol, do you get grades?

Oh wait, never mind

Well, I wish you good luck and good riddance of unnecessary irrational numbers, as those are not rational choices in life.

@iadvd Hello and welcome to my realm!

(I really want to automate that)

@iadvd If you are interested in my contest:

The big number (256) contest

Feb 10 at 23:00, 6 minutes total – 5 messages, 1 user, 1 star

Bookmarked Feb 10 at 23:37 by Simply Beautiful Art

@S.C.B. So from what you've told me, you just do things in class and take one final exam at the end, right?

iadvd

Hi @SimplyBeautifulArt just was curious about the

about the chat

Simply Beautiful Art

Ah, ok then

Well, feel free to browse.

iadvd

thanks! usually I am too shy to chat (I prefer writing questions) thank you for letting me browse. I might get used to it!

Simply Beautiful Art

lol, ok then. Do enjoy your stay and come back anytime

Starfall

@iadvd you're shy to chat online?

Simply Beautiful Art

01:24

@Starfall Wow, your still alive in here!

;-)

Starfall

i just played a stupid game of go where the opponent was behind like 20 moku and didn't resign until we played out the endgame

why are there people like this

Simply Beautiful Art

Some people are just out to make your life miserable man

in small little ways at least

Starfall

ikr

Simply Beautiful Art

repl.it/F7MS/34

S.C.B.

@SimplyBeautifulArt Yes.

Simply Beautiful Art

01:35

Ok. I wish they did things like that in America

at least at my school

S.C.B.

Hm. Not so good really.

Simply Beautiful Art

Why do you think so?

S.C.B.

One test basically decides everything. That isn't good sometimes. You need to have insurance in case you do bad.

Simply Beautiful Art

Ah, right, true

I suppose I prefer maybe 4 tests per class per year

iadvd

@Starfall @Starfall basically yeah... besides, English is not my mother tongue and that makes things difficult sometimes. :)

Starfall

01:41

@iadvd the only person here right now whose mother tongue is english is simple art

so there's no need to be shy

Simply Beautiful Art

Hi, I am a person

S.C.B.

@SimplyBeautifulArt Hi, I am breathing.

Simply Beautiful Art

@S.C.B. Hi breathing

:D

S.C.B.

Hi "a person".

Are you living?

Simply Beautiful Art

No

S.C.B.

01:46

When will you be living?

Simply Beautiful Art

That is not a computable number. Please ask a different question or try again with infinite running time.

13

Q: Could someone tell me how large this number is?

Context: If you guys didn't know, I'm running a nice little contest to see who can program the largest number. More specific rules if you are interested may be found in my chat room (click here to join). If you are entering, do note that I am accepting entries for quite a while (ignore all the ...

recursive-algorithms big-numbers hyperoperation

OMG

I FINALLY GOT AN ANSWER

S.C.B.

Where does the chained arrow notation $$f(x)=x \rightarrow x \rightarrow x \rightarrow x$$ Lie in the FGH?

Simply Beautiful Art

@S.C.B. Somewhere between $f_{\omega^2}(x)<x\to x\to x\to x<f_{\omega^3}(x)$

Leaning towards the $\omega^2$ side

I think

S.C.B.

So it is somewhat larger than your function.

Simply Beautiful Art

It is, I do think

S.C.B.

01:52

But I didn't make it anyway yet.

Simply Beautiful Art

But then I just figured out how to reach $f_{\omega^\omega}(x)$

So yeah.

S.C.B.

Lol I just read the best fantasy novel. (sarcasm)

Though it is in Korean.

Simply Beautiful Art

lol

What's your favorite novel?

S.C.B.

Would you like to read a translation?

Simply Beautiful Art

Maybe

Ugh, so many things to do

S.C.B.

01:55

In classical novels, I like Jane Eyre and Tess of the D'Urbervilles.

Simply Beautiful Art

And I honestly think sitting down and reading a book is good

S.C.B.

In fantasy novels, I like the KKC.

In modern novels, I like Catch-22.

Or Grapes of Wrath. Depending.

Simply Beautiful Art

I don't really read enough to know those people, but I'll trust your taste more than mine lol

@David Hello and welcome to my realm!

David

Hello hello!

Simply Beautiful Art

What brings you to this neighborhood?

David

01:58

The description says this is a room for "totally random people," I regret to inform you I was sampled from a very particular subset of the population.

Simply Beautiful Art

@Deedlit Thanks again!

repl.it/F7MS/34

Deedlit

no problem!

David

Was just interested in what may be being discussed in here...I have found your Q&A's to be quite interesting.

Simply Beautiful Art

^ And as I said, I just learned basic FGH

@David Ah, thanks

Just don't upvote me like crazy or you and I will get questioning looks

I'm not allowed to be so popular

David

@SimplyBeautifulArt anyway, just popped in to say hello. Perhaps you'll see me again the next time I'm procrastinating!

Simply Beautiful Art

02:03

Lol, ok then @David

@Deedlit If you don't mind, I'll leave the bounty up for some more time, since the contest and all

Deedlit

sure, I don't mind at all

Simply Beautiful Art

@Deedlit If I may ask, did you conclude the BEAF from the FGH?

Deedlit

yes

although you can see it directly

Simply Beautiful Art

XD Well it was not as obvious for me

Deedlit

you start from basically the Ackermann function, which is at level w in the FGH, and you iterate it 4 times from there, which gets you to w+4 in the FGH

Simply Beautiful Art

02:08

Besides FGH, what's another good thing to rank functions against?

Deedlit

I'm so used to the FGH

Simply Beautiful Art

lol, I think I will be too

Deedlit

you can use BEAF, which you can extend up to epsilon_0 naturally

Simply Beautiful Art

Of course. And then FGH beats BEAF?

iadvd

@Starfall @Starfall well that was the "besides" part of my phrase :) well then I will try another day to ask and talk more around here. Thanks for the words!

Deedlit

02:10

FGH goes as far as you care to define your ordinals

Simply Beautiful Art

As in FGH can keep going higher in a feasibly writable fashion while BEAF cannot?

All right...

The tricky use of ordinals in FGH was something quite new to me

Deedlit

Bowers has a more general notion for BEAF, but we've concluded that it is not well-defined

Simply Beautiful Art

which is why it took me a while to get straight

Deedlit

it's definitely tricky at first

Simply Beautiful Art

Yeah, I think I read about that on googology

Deedlit

02:11

:D I was about to mention the Googology Wiki

Simply Beautiful Art

The fact that FGH is so compact makes it... so much more manageable

@Deedlit Pft, what else would you get googol-ing "large numbers"?

Deedlit

true

Simply Beautiful Art

Trying to understand things without FGH and its ordinals was deadly XD

Honestly was killing myself

Deedlit

I'm glad it helped

Simply Beautiful Art

@baba Hello and welcome to my realm!

@Deedlit How long has it been since you started learning about googology?

(and I was actually going to ping you, since you were the best user on the big numbers tag as far as answers)

Deedlit

02:16

hmm... at least 5 years

Simply Beautiful Art

Nice

I haven't been studying "math" 5 years ago (was too young sadly)

Deedlit

I remember reading the results of David Moews' BIGNUM BAKEOFF, and I thought, "this is really cool"

Simply Beautiful Art

Haha, that's what I thought when I saw it

Deedlit

I think most people on the Googology Wiki are pretty young (teenagers mostly)

Simply Beautiful Art

His, uh, his final number. I don't even try imagining it. Not yet.

That was Rayo's number, right?

Deedlit

02:18

No, Loader's number

Simply Beautiful Art

Hm, Rayo's was the big number duel or something like that then

Deedlit

Rayo's function goes far beyond anything you could output in C

yeah, the big number duel

Simply Beautiful Art

Wait, does Loader's number have an FGH assigned to it?

Deedlit

it would be the proof theoretic ordinal of the Calculus of Constructions

which is probably bigger than any constructed recursive ordinal notation

Simply Beautiful Art

Oh....wait

Yup

Nope, Loader's number is pretty big...

The moment I see "bigger than TREE(3)"...

Deedlit

02:21

yes, MUCH bigger than TREE(3)

Simply Beautiful Art

Oh, wait, could you explain what the weird theta thing is in FGH?

I get $\epsilon_0$

and all those other similar things

Deedlit

an excellent introduction is here: en.wikipedia.org/wiki/Ordinal_collapsing_function

I'll be back in a bit

Simply Beautiful Art

Ah, thanks and ok

@Deedlit I may not be back by the time you are back

Oh

Oh god, so you are asking me to put ordinals in ordinals in ordinals.... inside FGH

Deedlit

back

Simply Beautiful Art

Happy Valentines to @amWhy and all others!

Deedlit

02:30

yes, the FGH makes you use infinite ordinals to make large numbers

Simply Beautiful Art

Jesus...

Deedlit

and the theta function makes you use uncountable ordinals to make large countable ordinals

Simply Beautiful Art

I should stop being surprised, but still!

Deedlit

and it keeps going on like that, to ordinals of higher and higher cardinality

Simply Beautiful Art

Why are things allowed to exceed FGH? It's beyond logically sane at this point XD

Deedlit

02:33

then you use inaccessible cardinals to diagonalize over cardinality

and Mahlo cardinals to diagonalize over inaccessibility

it's a big pyramid :D

Simply Beautiful Art

I mean, I get that its compute-able (somehow) and there are things beyond compute-able, but this is just too much

No, hold up

You just went to the inaccessible cardinals

and then went to the Mahlo cardinals like it was no big deal

WHY ARE THERE THINGS BEYOND INACCESSIBLE CARDINALS!?

God, wtf

why tf?

Deedlit

haha

anyway, before you leave

I encourage you to post on the Googology Wiki sometime

or come to the ##googology channel on IRC

Simply Beautiful Art

What would I post on it lol

Deedlit

whatever you want to talk about

like, if you have a question you can post it on your user page or in the forum

Simply Beautiful Art

ah, ok

Well, good night

Deedlit

02:39

good night

Simply Beautiful Art

And I wish you sane dreams

if you can sleep

Deedlit

same to you

Xam

04:36

Hello guys :)

Starfall

hi

Xam

I found this video and since tomorrow is San Valentin I decided to share it with you xd

The mathematics of love | Hannah Fry

►

The big number (256) contest

Transcript for

$Mathematics$ This is the Realm of Simply Beautiful…