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6:00 AM
i was but it was awhile ago n i dont remember what i was talking about (assuming i ever knew)
 
it's been 10 minutes...
 
my brain doesn't work right sometimes my train of though lasts milliseconds
 
@Semiclassical So, if I were to take a fish eye and turn it into a flat square, that represents -1? Well then... how do I multiply?
 
im on to thinking about PDEs
 
...
im still thinking about memory
and the fact that i might need to make my allocator bigger just to not run out of memory
 
6:03 AM
well don't forget...
 
i dont forget things
ever
 
Quick question: I am attempting to implement an equation from a paper (well, a power point based on a paper), and I have run into an equation, that by my reckoning is impossible to solve. However, this power point has been shown to a room full of professionals in the fields it relates too multiple years in a row, so I think its largely safe to assume the power point is not in error.
So here are the varables:
v is a 1x6 matrix, while M is a 6x6, and J is a 6x1. Lambda and t are both also 1x6 matrices. As far as I can tell, its impossible to multiply the product of M^-1 * J^T by (lambda - t).
 
what about when u run out of memory?
 
i only forget that which I have no use for and choose not to remember
 
6:04 AM
ffs
 
(sorry to interupt)
 
I'm referring to the allocator in my game.
array indices have a cap of 32000
so i might need to make it go into 2d arrays to bypass that limit
 
Whats T
 
@Faust7 learn linear algebra
 
that actually do know
 
6:07 AM
then you should always recognize transpose
 
well he used inverse in the same line
 
not the same thing
 
its bascially the same thing
 
dude...
no
 
@Faust7 its very not the same thing.....
Even I know that
:P
 
6:08 AM
transpose means to mirror the matrix along the corner
 
i know i know
 
inverse is just... division
 
in terms of algebra though there equivlant
 
@Faust7 No you don't.
NO
 
A^T A = I and A^-1 A =I
 
6:09 AM
lolno
 
since when?
 
Since always.
 
@Faust7 Stop stealing my help :P
 
@Faust7 A^T A = I only for a specific class of matrices called orthogonal matrices--in which A^T = A^-1.
 
6:09 AM
@GiantCowFilms nobody was helping you
 
Zee
Hey guys, is self studying from a math book that has no problems a bad idea?
 
Here, try [1 2; 0 1] as a matrix.
 
I was looking at the document first.
 
@TheGreatDuck Exactly, because they are helping Faust....
 
Now multiply it by its transpose.
 
6:10 AM
sigh*
 
Does that equal I?
 
no
 
@GiantCowFilms i was the only one here.... and nobody was helping faust. We were all BSing about my game.
 
@Zee Maybe not "bad" per se, but I wouldn't recommend it.
 
why the hell did i think those were the same
 
6:11 AM
@TheGreatDuck Now they are... they are teaching him about the difference between transpose and inverse.
 
I have no idea.
 
@Faust7 cause it's late at night
 
@Zee if you are to do so, try and prove its theorems as your exercises
 
@GiantCowFilms no. They're just correcting him cause he's being an idiot. We like to put people in their place.
 
lol
 
6:11 AM
and their place is to be at -100 rep
 
thanks duck
 
@TheGreatDuck I'm pretty sure there is mis-information in my question prompt. Please correct me!
 
I'm skeptical that J is actually a 6-by-1 matrix.
 
note: being or acting like an idiot doesn't make one in any way an idiot.
 
Zee
Makes sense, thx guys
 
6:12 AM
@TheGreatDuck That is a huge relief.
 
@GiantCowFilms i don't feel like doing vectors. I've been doing that for 12 hours straight trying to fix this stupid piece of junk I wrote.
 
Oh, derp. I can't read.
 
Out of curiosity, which book do you have in mind exactly? @Zee
 
@TheGreatDuck I'm also trying to fix a stupid piece of junk I wrote.....
 
O_n R
 
6:13 AM
@TheGreatDuck You must have quite a loose definition of "being"
 
...or maybe I can? I'm not sure.
 
First you're @Semiclassical, then Semicynical, now semiliterate...
 
@Fargle being as in acting like
not literally being something
 
@Daminark got eem
 
On page 23, they write J=[n | r x n]
 
6:13 AM
@TheGreatDuck Yeah, I'm just being pedantic. This being math chat and all.
 
Ther eis a group of matrices where A^T=A^-1
 
@GiantCowFilms dude. I said to ask someone else.
 
@Fargle Locally being
 
its just not true in general
 
but I don't know if they're writing vectors as column vectors or as row vectors
 
6:14 AM
@Semiclassical Indeed but page 30 kind of throws that out.
 
@Faust7 Indeed, the orthogonal matrices; i.e. those square matrices whose columns are orthonormal as vectors.
 
Zee
@Daminark Janich topology
 
@Faust7 The orthogonal group
 
im not even trying to help anyone. I just came here to tell semiclassical what was going on cause we were chit chatting earlier.
 
6:14 AM
@TheGreatDuck I know, know. I was just saying that to be funny.
 
Ugh this sniping... @Fargle
 
as long as im not entirely crazy
 
fair enough
 
Mostly I'm not impressed by this document, though.
 
@Daminark I'm the king of sniping, my friend.
 
6:15 AM
@Zee Ah, I've heard of that
 
when you can write as much code as i can in a day, you'll understand when you find out that the most basic little thing you based it all on is fundamentally inefficient.
:-)
 
@Zee If your heart's set on that book, whenever a theorem is presented, try to prove it before the book proves it for you.
 
Zee
@Daminark the only thing I don't like about it is that it don't covet Strieft van kampen
 
@Semiclassical Whew, I thought I was an idiot (although Duck seems to have cleared that up already). Although that PDF has been shown infront of a room full of industry physics engine developers at GDC multiple times in a row. I thought they would have noticed any errors.
 
That way you're essentially filling the void left by a lack of exercises.
 
6:16 AM
@giant hmm, I see what you mean. it's a 6-by-1 row for each contact
 
Exactly
 
What makes you choose it over Munkres/Willard?
 
It'd help a lot if they made clear what's a row vector and what's a column vector, though.
 
Zee
@Fargle my heart is not really set on it, too many pictures for my tastes
 
@GiantCowFilms I was actually referring to Faust with the idiot comment btw.
 
6:16 AM
@Zee Do Munkres, IMO.
 
I'm considering reading topology soon, so I'm trying to get the idea
 
lol
 
@Semiclassical Sometimes they clear it up. As far as I know all the velocity stuff is collumn.
 
@Daminark I'LL HELP
 
Zee
@Daminark am taking a course based on Munkres next semester so am looking for another book, plus Munkres is soo long
 
6:17 AM
@TheGreatDuck Again, I know, but I was just saying that to be funny, see my reply to the original comment.
 
yeah.
 
@Zee Were you there at the story when some algebraic geometer picked up this one book on geometric group theory and said "So many pictures it feels like pornography"
 
Zee
Lololol
 
lol wut?
 
And makes sense, try out Willard as well, I heard it's real good
 
6:18 AM
for it to make much sense, v and M^{-1} J^T (lambda-t) should be the same size matrices.
 
@Fargle I'm down for that :D
 
@Semiclassical I really think people who don't include, working, tested sample code in their papers and presentations that are designed to be implemented should be banned from programming.
 
@GiantCowFilms you have a very strange sense of funny. It bridges on being a troll. You walk a very fine line with that... I don't like trolls.
 
@Daminark I've been meaning to go through Munkres again anyway. It's been a long time since I did any point-set, and I was a sophomore undergraduate in a graduate-level class, so I was, no pun intended, outclassed.
 
6:19 AM
...
 
Zee
Williard ain't got no algebraic topology
 
@TheGreatDuck I've been called alot of things, but this is the first time I've gotten "Troll"
Ouch.
 
@GiantCowFilms That just shows how much of a troll you really are. /s
 
cries. Well at least I'm not an idoit because I act like one.
I like that quote....
frames it
 
Apparently all you need to do to bring this chat back to life is make a ridiculous statement and everyone wakes up.
 
Zee
6:20 AM
@Fargle did the course cover van kampen? Did you need much algebra for that?
 
Try Peter May's book for that @Zee... Hehehe
 
Zee
Nice try
 
@Fargle at one point I read the appendix of a manifolds book so I know a good number of definitions
 
@Semiclassical They should but aren't, hence my deep confusion.
 
And then there's the whole, extrapolating from metric topology which is probably the thing that this school has spent the most time training me in
 
6:21 AM
@Zee I don't think we covered van Kampen. We really only did chapters 2-5--we didn't even do Nagata-Smirnov or Tietze.
 
Zee
The book by singer seems badass
 
To clarify, the course I did was strictly point-set.
We didn't even discuss the supplementary material on topological groups.
 
just to make sure, M (and its inverse) are 6-by-6
 
One thing I will say, and it terrifies me that I'm agreeing with Zee, but Munkres drags on a whole lot
 
J is 1-by-6
 
6:22 AM
@GiantCowFilms to be fair, I said it was bridging on troll. As in the humor itself feels like the setup to a really bad troll stunt. To be fair, trolls are quite intelligent and devious. Good qualities. I just don't like them because they make me feel lesser.
 
@Semiclassical 6 by 1 (its long and short)
@Semiclassical As far as I can tell
 
It's like D&F-lite for topology
 
@Daminark It really does, but I like that it does to be honest. It makes it a good topology Bible.
 
? 1 row, 6 columns.
 
Zee
Lol I was just thinking that!!!
 
6:23 AM
Only @TedShifrin gets the privileged of showing off their superiority outside of the mods. After all, he's earned the right to do so. Granted, he doesn't do that very often.
 
@Semiclassical yes, I think so. At least before its transposed. We just discussed this.
 
usually you write it in that order because when multiplying AB you need the columns of A to match the rows of B.
sure? but that means J is 1-by-6.
 
@Semiclassical Yes...
 
TBF Ted is someone I'm totally willing to let act superior, and I don't really even think he does that.
 
@TedShifrin book on diff geo is beautiful
 
6:24 AM
@Zee this is interrupting our narrative of having diametrically opposed opinions
 
It seems to be pretty clear on that throughout the paper
 
He's just confident in his level of mathematical maturity, and has earned that confidence in spades over several decades of work.
 
compared to any other book i looked though anyway
 
thought you were disputing that.
anyways.
so M^{-1} J^T would be 6-by-1 as well.
 
I guess so....
 
6:25 AM
@Fargle I meant that he has the right to do so. I didn't say he does. AFAIK, he's the only retired Dr. of Mathematics that I've seen in here. So, he has mathematical superiority short of the authoritative superiority of the moderators.
 
But yeah that's why I think I prefer Willard, it's still got apparently good explanations and all, and it doesn't take quite too long
 
Yeah, to be clear I wasn't disagreeing with you, just harping.
 
But we need to end up with something that's 1-by-6.
 
Lel
 
Zee
General topology is overrated
 
6:25 AM
I've never read Willard myself. Munkres is one of only a few math books that I still have a hard copy of.
 
and there's no way to make that work :/
 
I mean, some people are into it, and it's good to understand the stuff since it forms a base for what comes later
 
ugh. I am up too late for this to make any sense.
 
@Semiclassical No a 1 by 6 will break it...
 
Lol, I've got like, 3 books on hard copy, I think
 
6:26 AM
im too burnt on matrices for today
 
I think one of the great strengths of Munkres is in its exercises.
 
wait no, I'm backwards
 
mostly staying up to finish rebuilding the code
 
its rows by collumns
 
right.
 
6:27 AM
wanna get rid of the latent inefficiency
 
so confused
 
(I can't compare this strength to that of Willard, but in my experience, the Munkres exercises really made me think.)
 
Let me restart here
 
so v is 6 rows, 1 column i.e. 6x1
 
Spivak Calculus, Sally's Fundamentals of Analysis, and Silverman's Introductory Complex Analysis
 
6:27 AM
@Semiclassical Yes
 
which means I was being silly too.
 
and J is 1x6
 
it seems like this would work out of lambda, t were just scalars.
 
@Semiclassical I was hoping that they were, but the seem to be decidedly not.
 
Zee
Narasimhan complex analysis is pretty damn good
Don't he teach at Chicago?
 
6:28 AM
I've got a soft copy of Narasimhan
 
@Daminark I have Munkres, a treatise on algebraic plane curves dating from the 1920s (with the printing I have being from the '50s), and a few lower-division texts for things like ODEs and linear algebra.
 
He used to, he's dead now
 
Zee
Damn...
 
He wrote that book based on how he taught graduate complex analysis here
 
actually, see page 45
They talk about lambda being straightforwardly 'positive'
 
6:29 AM
(Hope you could read that.)
 
I could
 
but that doesn't make a lot of sense if it's a matrix or a vector
 
@Semiclassical They do... but on page 7, they make it a 1x6
 
(I hope you could read that as well)
 
Yup
 
6:30 AM
i prefer actual books as opposed to digital ones
 
which is odd. Normally impulses are scalar.
:38127494 (removed)
 
that's a good point, alas
 
charges @GiantCowFilms for copyright infringement
oh the irony
 
Plagiarize! Let no one else's work evade your eyes...
 
bleh. I need to sleep
 
6:31 AM
Remember why the good Lord made your eyes
@Semi so you're not going through with the hallucination stuff?
 
why?
 
@Daminark Please send all legal and ethical complaints to our "Deal With It" department. You can find them on the ith floor.
 
And plagiarize, plagiarize, plagiarize! Although be sure to always call it please, "research".
 
maybe take a look at page 24 and its equation for lambda
that should imply what kind of a quantity lambda is.
 
@Semiclassical no I don't.
 
6:33 AM
successfully locates the ith floor somehow and but forgets what the actual complaint was at that point, so inputs a sequence of letters
 
I have no idea what you're on about, and for being annoyed at possible trolls you're acting a heck of a lot like one right now.
 
lol
Duck turtle
w8
Duck troll*
 
Zee
Ya he's a troll, a bad one too
 
sorry im tired brain not working
 
@Semiclassical My interpretation of the equation on P24 seems to be that it is a scalar. I think page 24 and 7 need to sort this issue out.
 
6:34 AM
Right.
 
...Rap Battle, maybe?
 
So yeah, that's bloody confusing.
 
@Faust7 I am not a turtle!
 
@Semiclassical The guy provided an email somewhere in one of his papers. I'm gonna ask him. This is a five year old presentation. I wonder what the odds are of getting a reply.
 
okay, really out now.
 
6:35 AM
Good night semi
 
insert frivolous message to get @Semi to stay yet longer
 
@Semiclassical bye!
Thanks for the help.
 
Jk see you
 
@TheGreatDuck but the picture is a turtle...
 
6:38 AM
@Faust7 no it's not. wat...
 
what is it then?
 
a guy
 
Zee
@Faust7 your not cool enough to call yourself Faust
 
in armor...
 
looks like a turtle with a dagger n a dice
 
6:39 AM
That's metal armor...
 
its a nickname from playing go, thats what the germans called me and it stuck.
 
Zee
Why did they call you that?
 
@Zee what if he is Faust?
 
Apparently it had something to do with how i played and something to do with an old story
sorry on repeat im kind of tired
 
Faust is the protagonist of a classic German legend. He is a scholar who is highly successful yet dissatisfied with his life, which leads him to make a pact with the Devil, exchanging his soul for unlimited knowledge and worldly pleasures. The Faust legend has been the basis for many literary, artistic, cinematic, and musical works that have reinterpreted it through the ages. "Faust" and the adjective "Faustian" imply a situation in which an ambitious person surrenders moral integrity in order to achieve power and success for a delimited term. The Faust of early books—as well as the ballads, dramas...
 
6:44 AM
go is a strategy game with many different styles of play, personally i prefer to fight and if possible kill my opponents ^^
 
go?!?
it's it a simple board game?
 
its like chess but older bigger board and more complicated
some exchanged are 35 moves deep just to get "fair result"
very fun strategy game if you enjoy that kind of thing sadly its alot hard to pick up then something like chess
 
not what i am thinking of
 
So we have:
- $\omega_1$, the union of all countable ordinals
- $\aleph_1$, the first uncountable cardinal
Now, how are $\omega_1$ and $\aleph_1$ equal? What axioms/theorems are needed to prove that they are equal?
cc @AlessandroCodenotti @Secret @SimplyBeautifulArt @LegionMammal978
 
i was thinking of one of those "move around the board and knock off pieces before they get to finish" games
 
6:48 AM
Go (traditional Chinese: 圍棋; simplified Chinese: 围棋; pinyin: wéiqí; Japanese: 囲碁; rōmaji: igo; Korean: 바둑; romaja: baduk; literally: "encircling game") is an abstract strategy board game for two players, in which the aim is to surround more territory than the opponent. The game was invented in ancient China more than 2,500 years ago, and is therefore believed to be the oldest board game continuously played today. It was considered one of the four essential arts of the cultured aristocratic Chinese scholar caste in antiquity. The earliest written reference to the game is generally recognized as...
 
not what i was thinking of
 
its big in asain can make millions playing it.
 
i didnt say it wasnt
i just said it wasnt what i was thinking of
 
oh i was just speaking generally really like the game ^^
 
6:55 AM
@Semiclassical it was all the function calls. It is now running immediately
like... instantly
 
congrats
 
im gonna need to develop a means to keep track of the allocation differently though
cause the stuff is still slow at super large numbers
like a 100*100*100 size cube
but to be fair... that's insane level stuff
these planets are meant to be small, i hope.
depends on what the other guy says
anyway
yay!
I'm going to bed.
 
gnight
 
7:54 AM
@LeakyNun it's a definition, cardinals are defined as ordinals for which $|\alpha|=\alpha$. (Where $|X|$ for a well ordered $X$ is the least ordinal $\lambda$ for which there is a 1-1function $\lambda\to X$)
 
@AlessandroCodenotti then how can we prove that $\omega_1$ is the union of all countable ordinals?
 
It is the least uncountable ordinal (it's defined as $(\omega)^+$), and every infinite cardinal is a limit ordinal so it's the union of the ordinals below
 
@Secret jou sun
@AlessandroCodenotti that makes sense to me, thanks.
I have another question: how do you know that $\aleph_1$ exists?
 
@LeakyNun wikipedia provided a short proof strategy by considering the set of all well ordered equivalence classes of the natural numbers. Each of these will be a countable ordinal. Therefore there are $\mathfrak{c}$ many of these thus this set can be bijected with $\aleph_1$. $\omega_1$ is the smallest of the ordinals with cardinality $\aleph_1$
 
@Secret we do not assume continuum hypothesis here.
 
8:07 AM
By Cantor's theorem we know that there are cardinals above $\aleph_0$ and since cardinal are ordinals the class of cardinals above $\aleph_0$ is well ordered, pick the least element
 
It appears just as alessandro mentioned, $\aleph_1$ is defined to be the cardinality of $\omega_1$ therefore the proof will be independent of CH
 
(The axiom of powerset is vital here, it is consistent with ZFC-P that $\omega$ is the only infinite cardinal)
 
@Secret you mentioned $\mathfrak c$ in your proof though.
@AlessandroCodenotti alright. Then, how can we know that $\aleph_\omega$ exists?
 
We define $\aleph_\alpha$ via transfinite induction
 
yeah, bad habit, I have a tendency to use that letter when it only mentioned "uncountable", but then forgot to think about whether CH is needed for some statement
 
8:10 AM
$\omega_0=\omega$
 
@AlessandroCodenotti so $\displaystyle \aleph_\omega := \left| \bigcup_{n < \omega} \omega_n \right|$?
 
$\omega_{\alpha+1}=(\omega_\alpha)^+$
For limit $\beta$ we define $\omega_\beta=\sup\{\omega_\alpha:\alpha<\beta\}$
 
@AlessandroCodenotti thanks
@Secret I have trouble understanding "well ordered equivalence classes of the natural numbers"
 
(And $\aleph_\alpha=\omega_\alpha$)
 
here's a better way to phrase it: Equivalence classes of well ordering that can be imposed on the natural numbers
 
8:12 AM
@Secret can you give me an example?
 
Anyway I have to go and study some topology now, bye everyone
 
@AlessandroCodenotti bye
 
Not sure, let's say 0,1,2,3,4,... falls in the equivalence class of $\omega$, 1,3,5,7,...2,4,6,8,... falls under the equivalence class of $\omega 2$
 
I think it would be best to just give me the link
 
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another. Any finite collection of objects can be put in order just by the process of counting: labeling the objects with distinct whole numbers. Ordinal numbers are thus the "labels" needed to arrange collections of objects in order. An ordinal number is used to describe the order type of a well ordered set (though this does not work for a well ordered proper class). A well ordered set is a set with a relation...
the link contains the section highlighted (initial ordinal)
 
8:18 AM
@Secret thanks, understood.
 
 
2 hours later…
10:45 AM
@LeakyNun They are not.
 
@LegionMammal978 $\aleph_1 = |\omega_1|$
 
@LeakyNun Yes.
More generally, $|\omega_\alpha|=\aleph_\alpha$ for $\alpha\in\mathrm{On}$.
Although that makes me wonder what the fixed point of $\alpha=\omega_\alpha$ (i.e., the limit of $\omega,\omega_\omega,\omega_{\omega_\omega},$ etc.) would be called
 
@LegionMammal978 I think it's just called the aleph-fixed point.
 
Suppose you were working on a mathematical problem, and for whatever reason, your solution used two different kinds of sets, which you call "curly sets" and "square sets".
So, $\{a,b\}=\{b,a\}$ and $\{a,a\}=\{a\}$ just as in normals set theory, but $[a,b]=[b,a]$ and $[a,a]=[a]$ as well. And you can have weird objects such as $\{a,[b]\}$ (nesting the two types of sets).
Now, someone comes along and says this is garbage. To them, all math takes place inside ZFC, and ZFC only has one kind of set.
To satisfy them, you need to somehow 'encode' your two types of sets into ZFC. How would you do it?
Hm, I suppose 'curly' and 'square' is kind of confusing, since curly braces are also used for "normal" sets.
How about 'angle' and 'square' (so, $\langle a,b\rangle$ and $[a,b]$).
@LeakyNun @Secret
I know how I would do this, but I'm curious how you guys would do it
 

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